I disagree that heavier people get more flats. The only tool that a heavy person might want to bring along (that a light person wouldn't) is a spoke wrench to fix wheel problems. Make sure it's the right size for your spokes & know how to use it.
For a day-long solo ride:
- tire levers (not metal)
- spare tube
- patch kit
- tire pump. I prefer an actual portable pump (Topeak road morph) because I can use it as many times as I want (no running out of air, etc.). Since I already weigh a lot the extra ounces don't matter to me. I can see the benefit of CO2 in self-supported race situation (faster, light weight, etc.)
- multitool (I have something similar to the Topeak previously listed). MAKE SURE that your multi-tool has the correct bits and pieces for your bike. In other words, it would suck if you needed a 6mm hex wrench for a seat post and your kit didn't have one. Obviously your multi-tool can't do everything but it should cover the basic adjustments (brake adjustment/repair, seat adjustment, & spoke wrench).
- 1st aid kit (real pain meds, large gauze pads, suture kit, etc.). This is in case of a major accident and I need to limp to the nearest phone or town. For smaller cuts and scrapes I just clean them up at home.
- Advil & Benadryl
- cell phone (charged)
- ID (I use RoadID + drivers license), credit card for purchases, five $10 bills (don't spend unless required, can be used to buy a ride into town, etc.)
- iodine tablets (emergency water purification, used only if desperate for fluids)
- emergency calories (gels, etc.)
- lightweight lock for bike (depending if I'm stopping in towns)
If I'm out with friends I carry almost everything listed above (except the lock). A pound here or there doesn't make a big difference for me / my level of fitness.