Problem With a rotating cylinder, applying weight to one side and not the other will cause it to rotate off axis and give it a 'wobble' likely causing undesired gravitational effects. Now clearly there's a certain scale at which the miniature changes in weight as someone walking around aren't going to affect the rotational axis of the cylinder but over the long term of building buildings or growing trees you might have to start taking that extra weight into account.
Question I was wondering what ways are there of counteracting this weight distribution.
One possible solution Couple of ways I can think of include having a 'ballast' in the hull of large tanks of liquid or movement of solids that apply the same extra weight to the opposite side of the OC to stop the wobble.
Edit This is not referring to the wobble you would get which flips the cylinder back and forth but rather the wobble around the central axis due to a difference in weight around that axis. Think of a washing machine with too much weight on one side, they tend to oscillate.