倾慕 is literary / written register - slightly old-fashioned and emotionally heavy. Common in novels, lyrics, and formal speeches. Conversational equivalent: 喜欢 (xǐhuān) or 欣赏 (xīnshǎng).
memory
Literally 'lean toward + admire' - 倾 means 'to incline / tip over toward', so 倾慕 paints admiration as your whole self leaning toward the object of devotion.
