I get to park my bike inside at work, too (and inside my apartment), so the only times I need to lock up are when I'm out and about.

I usually use a big chain (OnGuard Beast) because I can't always find a U-rack or parking meter that isn't already full of bikes, so I have to lock to a tree or light pole instead. To carry it on my short-hop city bike, I wrap it around the seatpost and lock it to the rear rack; for the road bike, I either wear it bandolier-style across my body or take a Kryptonite NY U-lock instead.

I don't really notice the weight much, but that's probably because I have a lot of weight of my own to carry.