The already given answers are correct, but I think explaining basic metabolism does not answer the problem of how big organisms can grow.
The argument about metazoan body size and the growing athmospheric O2 levels is that this latter process makes the diffusion of oxygen through animal tissue faster (because of the growing partial pressure of O2). This, in turn, made it possible for metazoans, which at the time had no elaborate body structures and no developed respiratory apparatuses, to actually grow larger, since it was possible for cells further away from the surface of an organism to respirate as well. Or, to put it differently, cell masses could grow bigger without risking anoxy in deeper parts of the tissue.
The problem with plants is not a very easy one to tackle, and I don't think there's a clear answer to this based on current knowledge. One must experiment with this and see what happens.
My guess is that the response of a plant lineage to grown O2 levels would be very dependent on the exact habitat the plant lives in, since for an evolutionary change to happen fast, there must be a clear evolutionary-ecological adaptive value it provides, and that is very dependent on environmental givens. Also, in recent (current) plants, respiration is a solved problem, so I'm not sure a plant would benefit in any way from elevated O2 levels. It would surely affect the working of RuBisCO as mentioned. Maybe an immediate response would be the spread of C4 metabolism within plants.