I play the occasional tourney online (usually am a Live low stakes cash player).

Playing a 10$ hyper turbo tournament.
I start this hand with 45BB MP with KK. (blinds 450/900 Ante 90).
I open for a little over 2BB.

Only the BB calls.

Pot: 5.44BB.
Flop JAK with 2 diamonds, I have no diamond.

He checks and I cbet for a 3rd of the pot, the BB calls.

Turn is an offsuit 5
Pot: 8.61BB.

He leads out for 4.96BB. I call.

River is an offsuit 2.
Pot: 18.54BB.

He continues for 13.9BB, I shove 36BB.

The question here, what calls my shove other than a straight or some lower set/2-pair (AJ only 2pair that makes sense)?
I have a very strong hand, but is shoving mandatory here? I've been stacked far too many times online in these spots, so I wanted to make sure.

I like a bigger cbet. The sort of stuff that calls is either too strong to fold (AX and better) or has good equity (JT). I wouldn't worry about balance because it's a hyperturbo microstakes tourney, and you don't usually play online.

Turn, you could flat looking to keep bluffs in and maybe induce a thin value bet OTR, but I'd probably prefer to KISS and raise.

River, I see what you're saying, I think it could go either way. You make money from JJ and 55 almost all of the time - 6 combos - but lose to the 16 combos of QT, and the 3 combos of AA. So they'd really need to be calling with a lot of two pairs. I guess that's what it comes down to, whether or not you can expect calls from those hands. Another consideration is that QT doesn't make too much sense, because it'd prefer to raise instead of take the check-call-lead line. And AA prefers to 3bet preflop. Interesting spot. I'm eager to hear what others have to say.