After the flop, the stack to pot ratio is 2.44 against the short stacked villain - this is the ideal number for your hand heads up plus position and when you hit your hand, you should be trying to get the money in (versus the short stack, not the button), which you did, unless you have a read to the contrary to not do so, which you didn't. I think you played it great. Why check the turn and allow villain to catch up by hitting a flush, trips, or something else? Why call the flop and allow villain to get away with a small, scared blocking bet?

Had this hand gone down against the lone, larger stack on the button, then, yes, I think a smaller raise or call on the flop would be wise to control the pot size as your SPR would only be about 8. But, "as is", I don't see how you can get away from it unless you had kept the pot smaller pre-flop, which would have not been optimal to begin with unless you have some better reads.