EVERYTHING BELOW ASSUMES YOU HAVE V'S RANGES CORRECT. (Personally I think this would be a very weird line for a hand like KJ, meaning if has 22 or 88, you're drawing dead. Other times he has 87, you hit 7 but he boats up. But I don't play micros so ymmv.)

There's two ways to look at it, the basic way, the EV of a shove, which you seem to understand, versus the merits of call vs shove. In a nutshell:

Let's assume you are debating between a call and a shove. For easy math's sake, lets say it's a 50BB shove on your part. The money over and above the call, your shove amount, you have 55%, +5.5BB EV. So it's slightly +EV. But what about the times you miss? If you just called the turn, you save 50BB 45% of the time. And on the times you hit? Even if he pays off just half the time, you'll win 50BB 25% of the time, for an EV of +12.5 BB.

In this equation we're not looking at the $ of the call, cuz you're going to put that money in either way. It's just the extra money we're interested in.

So yes shoving is +EV, but depending on his ability to lay down a hand, it might be more +EV just calling the turn and shoving rivers that you hit.

PS Don't be surprised if a coach comes in and tells me my math is wrong.

I think you're being over optimistic that people will be raising Kx on a turn which pairs the board.

A lot depends on the stakes. In the micros players are generally passive as a rule, so if you're facing a large raise and have no showdown value you can fold without much worry without reads. You said check raise but stated that villain was on the BTN, so that's not possible, meaning that your draw has much less value being OOP yourself, not to mention the board is paired already.

This idea of reraising on the turn works well in super aggressive games where we expect villains to be bluffing a lot more, but this simply won't happen in micro stakes games.