@ragingloli is right. “Con” as in “pro and con” comes from “contra”, meaning “against”. The “con” in constitution, congress, etc. means “with” or “together”. The root -stitution comes from the Latin verb statuo, which means “I set up” (hence “statue” or “statute”), so a prostitute is someone who sets themselves up in public (the word is pretty far removed from its literal origin) and a constitution is something set up together.
I get the joke; just posting this in case anyone was curious :)