Why does it say "Asher Yaladt Li"?
Rashi citing Tanchuma 1 : A man had five sons. Four were to serve idolatry, and one was designated for Beis ha'Sefer (to learn Torah). If he comes to offer one of them to Molech, he offers the one designated to learn Torah.
Rashi: These are the Bechoros ? "va'Atamei Osam b'Matenosam b'Ha'avir Kol Peter Rechem" (20:26).
Radak: They entered My Bris, and they were for Me. You took them from Me and from My Torah!
Radak citing Targum Yonasan: How do you increase to anger Me, Keneses Yisrael! You take your sons and daughters, who were destined to beget Kodesh children in front of Me?
Malbim: Initially they are Banaayich and Benosayich. Really, they were yours, and not mine. It says Yaladt Li, for attributed them to me, for they grew up in my house.
I did not find this there. Eichah Rabah 1:3 brings close to what Rashi cites. (PF)
Did she offer her sons?
Yes (refer to 16:20:1:1). Radak ? she slaughtered them so the fire will consume them, and to pass them to Molech ? "Lisrof Es Bneihem v'Es Benoseihem ba'Esh" (Yirmeyah 7:31).
Malbim: Yes. Now it describes in the days of Achaz, when they served idolatry openly. He passed his sons in the fire to Molech.
What is the question "ha'Me'at mi'Taznusayich"?
Radak: Is it a little that you anger Me with your sons and daughters who were to Me, and you slaughter them to [the idols]?
Malbim: It was not enough that you took your sons that you bore to me 1 in Zenus ? therefore, you increased?
Malbim explained, they are not mine, just you attribute them to me, for they grew up in my house.