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