I have a friend who carries a bike lock and bus fare card for an urban repair kit. Lock the bike up, take the bus home and come back with the car to pick up the bike. That's light!

I carry:

Park MT-1 multi-tool. It has enough length for good leverage on stuff like a seat bolt and weighs 1.6oz
Leatherman Skeletool CX pliers-based multi-tool with knife blade, screwdriver bits
Patch kit
New inner tube
Topeak MiniMasterBlaster tire pump
Zip ties
An old chunk of inner tube for shims, tire boot, rubber bands etc
Spare batteries
Road Wipe hand cleaner towelette
Rubber gloves
Small roll (hiking style) duct tape
Small vial chain oil

I have a small Park Tool CT-5 chain tool that is 2.5oz, but I don't carry it as a habit. I could see hauling chain stuff for remote trips and singletrack where you might wipe out a rear derailleur on a rock and you could rig for single-speed to get home. Drivetrains should be carefully inspected before any trip and well maintained. Chains usually give good warning before failure.

We tend to pack for fear and you have to reach some balance point of preparedness over weight and bulk. A local trip is a whole other thing than bikepacking Peru or or the Continental Divide Trail-- the difference being spare parts and the tools to use them. If you are going remote, I would be more concerned with having the classic hiking "ten essentials" and shoes I can walk out in. 20 miles in cleats wouldn't be fun!

Carry options: larger seat bag, handlebar bag, fanny pack, small backpack, messenger bag, rear rack and trunkbag/panniers.

My favorite urban combo du jour is a grocery style pannier on my rear rack with a backpack dropped in the pannier. I can haul my U lock on one side of the rack and the cable in the bottom of the pannier with the backpack. The advantage is in loading and unloading. Trunk bags are great, but having to load/unload them is a pain. The pannier is zip-tied in place to prevent casual theft and I can just pick up the backpack and go. If I end up hauling stuff (like groceries), I can still wear the backpack. That gives plenty of room for tools, spare clothing, camera, snacks, etc.