Is Gavhus ha'Lev permitted?
Malbim: Sometimes it is good, e.g. Yehoshafat - "va'Yigbah Libo b'Darchei Hashem" (17:6). Uziyah became haughty more than the proper amount.
What is the meaning of "Ad Lehashchis"?
Metzudas David: Until he was corrupted to do evil due to his great pride.
Malbim: The king runs the country, and the Kohen 1 oversees Das (Torah law). The king could not do anything new without the Kohen's consent. Uziyah wanted that also Das will be under his jurisdiction, for he wanted to destroy Das.
Chachamim and the Sanhedrin oversee Das! The Torah calls Chachamim "Kohen" ? "Asher Ya'aseh b'Zadon l'Vilti Shemo'a El ha'Kohen" (Devarim 17:12). (PF)
Why does it say "va'Yim'al"?
'Rashi': An expression of Me'ilah applies, for he was Shogeg 1 ? "Ki Sim'ol Ma'al v'Chat'ah bi'Shegagah" (Vayikra 5:1).
The Kohanim warned him (verse 18)! Perhaps initially he was Shogeg. (PF)
Why did he enter the Heichal?
'Rashi' citing Tanchuma Noach 13): He thought that it is proper that the king serve Melech ha'Kavod.
