I don't call you handsome, sir, though I love you most dearly: far too dearly to flatter you. Don't flatter me.

This quote means that the speaker loves the person they are speaking to very much, but they won’t express it through a compliment because they don’t want to be overly flattering. The speaker loves the person enough not to exaggerate their feelings and wants them to know that their love is genuine and not due to flattering them.