Blackjack Mistress Issues Apology to Mrs. Weiner

6/8/2011 12:45 AM PDTby TMZ Staff Rep. Anthony Weiner's Vegas-based cyber mistress felt so bad about her involvement in "Weinergate" -- she typed up an apology letter and mailed it off to Mrs. Weiner ... TMZ has learned. In the letter, obtained by TMZ, blackjack dealer Lisa Weiss tells Huma Abedin she wants to express her "deepest apologies for conversing with your husband Congressman Anthony Weiner."Weiss adds, "I honestly meant no harm and I hope that you and Anthony can work through this."Before signing off, Weiss noted, "I still remain a huge supporter!"So we gotta ask ...