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.”
A multitool is a highly versatile piece of repair equipment that can address most of your maintenance needs. Ideally, you should use it before a ride to tighten and adjust everything properly, but sometimes it’s necessary on a ride as well. If you encounter a loose screw, realize your saddle height is not right, or that your brakes need tightening, you will be happy to have it.
Spare tube: Sometimes, a tube is just too damaged to be patched, or has had a failure such as the valve stem breaking off which isn’t something that can be patched. To save weight and space, I usually keep a lightweight version of the right size tube for my bike. Since one of the first things I do with most bikes that I own is switch them over to heavy-duty thorn resistant tubes, I just take one of the originals and put that in the toolkit.
Brakes come in a variety of designs depending on the age and style of your bike. Rim brakes offer more modulation but have less stopping power, so are more suited to riding on the roads. Disc brakes can provide huge amounts of stopping power so are best suited to off road riding, although ‘V’ rim brakes are also well suited to mountain biking. All brakes use a friction system to stop the movement of the wheel, so regular checks of the contact pads should form part of your regular cycle maintenance.