The spare apparently weighs approximately 75 pounds from a quick google search. The wheel apparently is about 25 pounds of that, and so the tire would be about 50 pounds. The air in the tire does weigh something, but it's a small enough amount to be neglected in these rough computations.
Removing the wheel from the tire to save weight makes no sense in my opinion; draining three gallons of water out of the fresh water tank would accomplish the same thing. I wouldn't want to travel without a spare, even with roadside assistance, as not having one could easily turn a half hour service call into an all day affair, particularly if it's more an automotive sort of service truck that gets dispatched rather than a big rig truck mobile service.