Gemara

(Mishnah): If one finds Tefilin [on Shabbos where they are prone to be disgraced] he brings them in one pair at a time.

Inference: This is unlike R. Meir, who permits wearing as many clothes as desired at once!

Rejection (Rava): Our Mishnah can be R. Meir. In both cases he permits Derech Malbush (the normal way of wearing), like on a weekday:

On a weekday one wears as many clothes as he desires, but only one pair of Tefilin.

Shabbos 59b - Question (Ravina): May one wear Kamra (a belt with gold and gems woven inside, or it is all gold) and also a belt?

Answer (Rav Ashi): This is like wearing two belts.

147b (R. Chiya bar Aba): Bathhouse attendants may bring towels for women to the bathhouse [through Reshus ha'Rabim, via wearing them], on condition that they cover the majority of their heads and bodies with them.

120a (Beraisa - R. Meir): If there is a fire on Shabbos, one may wear [clothes, to save them], go out, and remove them; wear, go out, and remove them, the whole day;

R. Yosi says, he may not wear more than 18 garments - a cloak, a housecoat, Punda... a belt on his loins...

Rishonim

Rosh (6:5): Rashi explains that a second belt is a load, so it is forbidden. This is only if they were one on top of the other. If a garment separates between them, it is permitted. A support for this is 120a. It lists, among the 18 garments that one may save, Punda and a belt. Rashi explains that Punda is a belt.

Rashi (59b DH Trei): Talmidei R. Yitzchak forbid two belts. This seems correct, for on 120a, we permit only one belt. Talmidei R. Levi permit.

Tosfos (59b DH Trei): Rashi brings an opinion that forbids two belts. Even though Punda and a belt are counted among the 18 permitted garments, that is when a garment separates between them. Two belts, one on top of the other, are forbidden. This is unlike wearing many garments due to the cold. Here, there is no benefit from a second belt. It is not normal to do so. It is a load.

Rashi (120a DH Punda): Punda is a hollow belt worn over one's garments.

Sefer Chasidim (773, b'Sof): When one walks in Reshus ha'Rabim with a belt, he must gird it. If not, he carries it without need.

Poskim

Shulchan Aruch (OC 301:36): One may go out on Shabbos with two garments one on top of the other, whether for his own need or for the need of his friend.

Beis Yosef (DH v'Chasav): The Roke'ach (47) learns from R. Chiya bar Aba that one may take out on Shabbos a garment for the need of someone else, if he wears it over all his clothes. However, two belts are forbidden. Also Kolbo permits wearing a garment that he does not need, in order to take it out for someone else, even to Reshus ha'Rabim. This is clear from the laws we mentioned.

Beis Yosef (DH uv'Kolbo): Tosfos, the Rosh, Mordechai, Semag, Semak and Sefer ha'Terumah permit two coats. However, the Mordechai (347) says that R. Yo'el forbids two Maktorin (jackets) one over another for the sake of his friend. It is not clear to me Maktorin (how it differs from a cloak - PF). In any case, since many permit, we follow them.

Beis Yosef (DH u'Mah): The Tur brings that Sefer ha'Mitzvos forbids two cloaks. I did not see anyone say so. The reason is that there is no benefit from the second cloak and it is not normal to wear it, so it is a load, like Tosfos and the Rosh say about two belts. However, Tosfos (147b DH Tzarich) says that Sanbita is a very thin garment. One must tie the ends below, so the wind will not blow it, or because it looks like a load and not like a garment, unless it is tied. Tosfos permits even though it is very thin and he does not benefit from it, since he carries it Derech Mabush (in the way of wearing).

Gra (DH Mutar): Eruvin 95b proves that what is permitted to save from a fire is Derech Malbush.

Shulchan Aruch (ibid.): It is permitted whether they are two shirts, two coats or two belts, even if no garment separates them.

Beis Yosef (DH uv'Kolbo): Kolbo says that the Yere'im (274) forbids even if there is a garment in between, if he needs only one belt. A second belt was permitted only regarding a fire. The Rif and Rambam did not mention two belts. This connotes that they explain 'do you ask about two belts?!' to mean that it is surely permitted. Since both of them agree, we hold like them.

Beis Yosef (DH Kasav ha'Agur): The Agur and Shibolei ha'Leket permit going out with two [pairs of] socks or two turbans due to the cold.

Rema: Some forbid two belts unless a garment separates them.

Beis Yosef (DH Shtei): The Tashbatz (47) forbids two belts without anything in between, like Tosfos and the Rosh.

Kaf ha'Chayim (207): There is no benefit of warmth from two belts. If the custom in a place is to wear two belts, it is permitted. However, Eliyahu Rabah says that perhaps we are not concerned for their practice, and the Halachah is based on normal people. Tosefes Shabbos says that if we are unsure what is the majority custom of the world, we follow the local custom.

Beis Yosef (DH Kasuv b'Shibolei): Shibolei ha'Leket also says that the stringent opinion forbids two belts only when they are one on top of the other, but not if his garments are long and he needs a belt between each. Our women have dresses with belts sewn to gird themselves at the hips. After, they wear another belt of silk or silver. It would be better that they wear only the latter. The belt of the dress is not as important that the belt of silk or silver. (Magen Avraham 49 - in any case,) the belt of the dress is not considered a load, for it is connected to the dress and Batel to it. One may wear a Kilah (canopy) in Reshus ha'Rabim with its straps [for they are Batel to it - 139b]. Shibolei ha'Leket also says that if one has two belts in his pants, one with a drawstring, and one that attaches above at the hips, it is permitted if the stitching of the pants divides them into two belts. If not, it is forbidden, like two belts one on top of the other.

Taz (25): I do not understand the Isur. We forbid two belts because one does not need both of them. Here, surely both are needed!

Taz (25): The Isur to wear two belts does not apply to women who gird themselves with a belt, and afterwards lift the garment a little and wear another belt below. Both of these belts are needed. Also, a garment separates between them. However, I am concerned lest this is like Marzev (a string tied to make a hem), which we forbid above. The part that is folded is like a Marzev. Regarding this, we can say that it is better that Yisraelim transgress b'Shogeg [than b'Mezid].

Gra (DH v'Yesh and DH Ela): This opinion learns from R. Yosi. Even though the Halachah does not follow R. Yosi, this is because Chachamim were lenient regarding a fire. If not [for a fire], R. Meir agrees with R. Yosi, like the first opinion in Rashi (59b). The first opinion is like the latter opinion in Rashi.

Mishnah Berurah (133): The Poskim connote that all agree that the Isur of two belts is only mid'Rabanan, since it is Derech Malbush. The Isur is only because it looks like a load. All the more so, wearing a handkerchief on the belt, which is not the normal way to gird it, is forbidden. The Chayei Adam says that even the first opinion forbids this. Since people do not gird this way during the week, it is evident that he schemes in order to take it out. It is forbidden even to Karmelis. The Taz (14) counseled to attach the end of the handkerchief to the end of the belt through a bow, and then it looks like a long belt. He girds also with the handkerchief. Based on what is explained below, he can gird the handkerchief through a garment in between. I.e. if the belt is above, he girds on the pants. However, he may not tie the handkerchief around the leg. This is not Derech Malbush at all. Rather, he does like we said, or ties it around the neck Derech Malbush.

Mishnah Berurah (134): Where the custom is to gird a belt under [the garment] that does not look nice, and a nice belt over it, and the latter girds nicely on the former, or the latter is short, it is permitted. Some women gird themselves with a belt, and tie another belt on the wide garment below to lift it from the ground, so that it will not get muddy. This is permitted, for there is a need for this.

Mishnah Berurah (135): If a cloak has a belt sewn in, and he wants to tie a belt over it, the former is not a load, for it is Batel to the garment, since it is sewn in. However, if he girds both of them, the belt [not sewn in] is a load.

Kaf ha'Chayim (204): It is a load because it is not needed.

Rema (ibid.): It is proper to follow this. One may wear two socks one on top of the other.

Gra (DH v'Chen): Based on what we said above, this is difficult. We permit only one pair [of socks regarding a fire]! Rather, he [the Rema] rejects the above proof, for we hold like R. Meir. He explains that two belts are forbidden.