Wheels are typically the major weight factor after the frame.
Tyre also yes, but there’s less you can do about that unless you’re going to sacrifice durability & puncture resistance for lightweight.
Wheels though, can be 500g difference in a set between lightweight and heavy ones. Light wheels don’t have to be carbon. Plenty of alloy wheels that are light, and even tough. Problem is they tend to be a lot more expensive also. Carbon wheels are a different thing. It’s more about stiffness than weight.
Still, over 30lbs in a carbon bike. Is it just carbon frame? It also depends what carbon it is as not all carbon is the same. Cheaper carbon tends to be heavier and lighter is more complex to produce but retain the strength, thus more expensive. Other carbon bits? Carbon cranks and bars make a difference. Levers and bits on mechs, less so.