First, carbon. You already know you don’t need it for your casual weekend pursuits, because you’re not counting ounces the way a professional road racer would. But to quote an article from Velonews, “Remember that professional athletes operate in an entirely different environment than the rest of us. They are all very close to each other in terms of fitness, and they are also all very close to being the absolute best a human being can be. In short, you’re much better off upgrading your legs and dropping body fat through proper training and diet.”
Basic first aid supplies: A few bandages of varying sizes. 6 Aspirin, or other OTC painkiller of choice. A few alcohol pads in sealed foil packs, useful for cleaning grease off grease and grit off of the bike, and also cleaning cuts on yourself if you take a spill. 1 day supply of any prescription drugs you need to take regularly. Wrap these up in tinfoil and tuck away. It might just save your day.
Broadly speaking there are two major wheel sizes – 700c for road bikes and 26 inch off-road wheels. However there are a whole variety of older, less common wheel sizes and of course fold up bikes have much smaller wheels altogether. Repairing a puncture is not an emergency! It’s a basic procedure that every cyclist should be able to to perform, but doing it correctly involves more steps than many people realise. Wheel building is often seen as the most artful skill in bicycle maintenance, and separates the professionals from the amateurs but that doesn’t mean you should consider it out of reach. Truing a slightly misaligned wheel is a cycle maintenance job that almost any cyclist can perform.