Against good opponents, you'd likely want to play a mixed strategy of checking and betting with your sets on this board. (In other words, the EVs of checking and betting are equivalent at equilibrium.)
However, in this case you are almost certainly not playing against good opponents.
As described, you're playing against overly tight, straightforward players who have a tendency to fold too frequently. Let's call them "Walter Nitty", with apologies to Thurber. So, how do we best exploit them? Well, we need to give them as many opportunities as possible to make folding mistakes, so we should be betting in this spot very frequently.
The construction of our betting and checking ranges on this flop will depend on our bet sizing, so what sizing should we use? Well, many players at these stakes are very inelastic in their continuation ranges -- not only do they fail to call with enough hands, they also don't correctly adjust their continuation range to the size of bet they face. If they continue with a range as if they faced a 1.5 pot bet, even when you only bet 0.33 pot, then they're giving you a licence to rob them blind. So against the Walter Nittys of the world, I tend to prefer c-betting with a comparatively small sizing, but with a very large fraction (approaching 100%) of my range.
How small? Well, if you were in position on a rainbow flop, I might go as small as 0.25 pot. In this case, though, as "monkey in the middle" on a flop with a flush draw, something in the 0.35 to 0.40 pot range seems about right. Half pot is starting to feel a bit too big -- I'll have to incorporate more hands into my checking range, which sacrifices the money I make from the Nittys' folding mistakes in the hopes of gaining more from my value hands.
This line has a number of advantages:
- I give my opponents maximum opportunity to make folding mistakes,
- I pay a comparatively small price to bring my opponents' holdings into much sharper focus, and
- When I bet, I keep my opponents' knowledge of my range as wide and ill-defined as possible.
The principal drawback of this approach is that the smaller sizing makes it much more difficult to get stacks in by the river. But winning many more small pots when they fold incorrectly should more than compensate for the smaller amounts brought in by your monsters.
To be sure, it kinda sucks when you bet 0.35 pot with your 22 and they both fold, but you're more than happy to see the same result when you bet 0.35 pot with, say, 7h6h, or 33, or QcJc, or ...
If you get called by one or both of them, now you know where you stand, and you can revert to more standard play with larger sizings (say 0.75 to full pot bets) on the turn, and a more usual balance between your checking and betting ranges. There could be specific turn cards where you might opt to slowplay some of your sets at this point (say, to help balance your checking range if you find yourself out of position against just the button), but most of the time, once you know your opponent is "hooked", it's time to keep up the betting pressure.
Aside: If your opponents were instead too loose and making lots of calling mistakes, the same logic would lead to exploiting them by adjusting your sizings upwards -- with your sets, you'd then be aiming for three streets of value in the form pot-pot-jam.
