Probably one of the few times I've ever disagreed with the venerable Thunderbird+... but then we've all had different experiences, I expect. Your example is obviously a hybrid of some sort. Grafted, as T-bird says, with a "knot" at the graft point. The expected results grows from above this point. My experience is that once, for whatever reason, such a rose begins to send up shoots from below this point, it will never perfom as intended. My action has to be dig it up and start over with a fresh one. It seems as though all the energy of the plant goes into growing the wild root stock and it will no longer bloom... at least as it should. The reason you get only small blooms is that the original root stock is probably a variety ofrosa the original rose stock from which almost all of our modern roses started and produces flowers of only 5 petals. Best of luck, though!