Nice hand.
To think about this situation properly, I believe you need to think about your entire play in the BB versus a BTN open. What hands are you 3-betting? What hands are you flatting? Do you have a 3-bet bluffing range versus this villain in this spot?
Once you know what your overall preflop flatting range is, think about what you are going to do with what parts of that range. I assume that your donkbetting range is nil, so there will be three parts: check-fold, check-call, and checkraise. What value hands are in your checkraise range? How many bluffs do you suppose you need to balance your value checkraises?
At a glance, T
9
on a K
Q
4
board looks like a reasonable candidate for checkraising. We have essentially no showdown value unimproved, and we do have equity from our gutshot and backdoor flush draws. That said, we do not have enough equity to call down.
But to make that judgment better, what you really need to do is work the problem I outlined with a bunch of hands in a bunch of BTN vs BB situations, and learn to get a feel for what is right, so you can take that feel with you to the tables when you play.
Your bet-sizing seems reasonable to me, but take my judgment with a grain of salt, because I don't feel fully up to speed with my own bet-sizing.