I carry a pump, CO2, and 2 spare tubes, tire boots, tire tools, and a patch kit.

The pump is to get started so you can check for a pinched tube. CO2 in case pump breaks or I am too tired to use the pump or possibly injured if I flatted on a hill and wrecked. 2 spare tubes because if you are not careful you can twist off a valve stem using a frame pump or you can hand someone a tube without worrying about flatting. Finally, patch kit in case you are on a group ride and unexpectedly hit some glass that causes several people to flat and resources are spread thin. Maybe overkill, but if you ride a lot of miles and group rides it will come in handy some day. There is nothing worse than being in the middle of nowhere and having to walk or call for help.

If you are worried about weight, at the minimum I would carry a mini-pump and spare tube. CO2 would not be a bad idea. Some mini-pumps can attach a CO2 cartridge so you do not have to have the CO2 inflator taking up space and adding weight.