How much would a ticket for broken headlights and missing proof of insurance raise your insurance rate?

If you were stopped and couldn't produce proof of insurance the vehicle got impounded so depending on your coverage limits you may be looking at about a 20% increase right there for about 12-18 months. That's what they get in return for the towing/storage fee which usually they pay in full for you if you were actually insured.

As far as the headlights are concerened, that depends on how long it went unfixed and if you knew about it prior to the stop. If no accident was involved ironically it may have no impact on it whatsoever but sorry they won't pay for the light to be replaced! Nice thought though isn't it?

Always keep your insurance in the car someplace secure and in a place in plain view so the police won't panic if they see your hands leave their sight to retrieve papers.