Two weeks sounds awfully fast to heal two or three broken ribs. As the no doubt better informed among us say, expect longer.
Same old bottom line: it's your story, so your character can be as tough as you want.
My experience: Guy kicked me in the ribs once and I'm pretty sure one of them broke. I say “pretty sure” because it hurt to breathe, cough, sneeze, laugh, turn-twist upper body, for at least a couple of weeks after that. More like four weeks, as I recall. And I didn't go to a hospital to get checked out. I was young and stupid and didn't know any better, so a week or two after that sparring incident, I was sparring again, but I was much more protective of that angle than any other, and my left arm wasn't used much as it stayed protectively welded against the questionable-rib side in a covering position. I mostly relied upon kicking people away from me, or the occasional straight right.
Was this a serious break? I have no idea, but I now have a gravel-like lump under the skin where the rib probably broke, and had I soaked up another bone-breaking shot in the same place, I suppose I might have been out of the fight. See, the first time around, I knocked silly the guy who (I suspect) broke the rib. He gets woozy and quits, but feels fine a few minutes later. Meanwhile, just breathing hurts me, and for about a month. But my ability to continue fighting lasted for the moment, while I was still full of vim, vigor, and energy. That week or two later? I wasn't nearly as effective. And to get blasted in the same area? That hurts just to think about.
Another example. One of the black belt students broke about four of the ribs of one of my instructors while sparring, but the instructor took the student down and ended the fight, despite a lot of discomfort. Student wondered how he was able to do that. Instructor said: You must learn to fight through pain. The fight doesn't end just because you're hurt, nor does it end just because you've hurt your opponent. It ends when one of you can no longer continue. If you pause because you see that you've inured your opponent, you are just as vulnerable in that moment as he is.
Or something like that. More ribs certainly broken than mine, the instructor was out of sparring action for a good long time, tanked up on pain killers so he could sleep. Could he have fought again, two weeks later? I dunno. That dude's tough as nails, but his x-rays showed some serious breaks. I suspect mine wasn't nearly as bad.
So could your fictional character fight a couple of weeks later? Sure. No problem, it's fiction, after all. Would it be realistic? Well, in my meager experience, doable, but with great discomfort and at a performance disadvantage directly proportional to the amount of damage sustained. Two or three broken ribs? Good luck, hale fellow.
In light of this:
I'm aiming for putting him in a position that he just can't fight back.
I suspect you've already hit a very good nail on the head. Three seriously broken ribs? Two weeks later, knee bashed in the same area? Dude's in serious trouble. In fact, he was probably in serious trouble even before the new hit.