This sentence can be fixed in one of the following ways: get rid of the conjunction or replace the semicolon with a comma.
Semicolons aren’t used with conjunctions except when you’re using semicolons as a “super-commas” with a list (this is the “semicolons in a complex list” rule from CMoS, section 6.58), and you — intelligent person that you are — have used an “Oxford semicolon” before the conjunction between the next-to-last and last items in the list. (Example: Her favorite foods are pizza with chicken, spinach, and onions; cheese cake with strawberries; and pot roast with potatoes and carrots.)
“You’re a weapon; weapons don’t weep.”
“You’re a weapon, and weapons don’t weep.”
(Mercenary Proofreader prefers the latter because semicolons in dialogue look weird.)
You could also replace the comma from the original with a period: “You’re a weapon. Weapons don’t weep.”