Respecting, in this use, means “about” or “on the subject of.” You meet it in careful, old-fashioned, or legal English: “Respecting your letter…” means “about that letter.” It does not, here, mean that you feel honour toward someone.

Respectingrespecting in this use在這個用法裡 means "about" or "on the subject of."意思是「關於」或「就……而言」。You你 meet it in careful, old-fashioned, or legal English會在講究、老派或法律英文裡遇到它 "Respecting your letter…""Respecting your letter…" means "about that letter."意思是「關於那封信」。It它 does not, here, mean that you feel honour toward someone在這裡並不是指你對某人心懷敬意。

Though actually, it began as the -ing form of the verb respect, in an older sense “to look toward / to consider,” and then froze into a preposition.

Though actually不過其實 it它 began as the -ing form of the verb respect一開始是動詞respect的-ing形式 in an older sense在比較舊的意思裡 "to look toward / to consider,"是「朝向看／考慮」 and then froze into a preposition後來才凝固變成一個介系詞。

Younger speakers almost never say it this way in casual talk; they say about, regarding, or as for. You will still find it in formal letters, older books, and some official notices.

Younger speakers年輕一輩的人 almost never say it this way in casual talk在輕鬆的對話裡幾乎不會這樣講 they大家 say about, regarding, or as for會說about、regarding或as for。You你 will still find it仍然會找到它 in formal letters, older books, and some official notices在正式書信、較舊的書和一些官方公告裡。

A different, everyday sentence — “He is respecting her wishes” — is just the verb going on now, and that is not this sense.

A different, everyday sentence另一個不同的日常句子 "He is respecting her wishes""He is respecting her wishes" is just the verb going on now只是動詞現在進行式的用法 and that is not this sense跟這裡講的意思不一樣。