I once read about guy who had his bike lifted by a passing car while he'd stopped for a pee. That's probably a bite extreme, and the sort of bad luck you can't do anything about, but it's probably a good idea to take a cable lock to lock your bike to something while you are in a pub.
Insurance is definitely a good idea, but when I checked, if you have an expensive bike then the chances are they will require you to use a Sold Secure lock to lock it to an immoveable object - so don't expect to save much weight as good-quality locks are pretty similar in weight.
I use a hip-lok which is a decent size lock but designed to be worn round the hips like a belt so you don't notice the weight so much.
I was once stopped by a casualty nurse who saw me riding with a lock around my waist - she said that she'd seen cyclists come in with their pelvises smashed up as a result of being in an accident while riding with a lock around your waist. Made sense to me.