Let's assume that he 3bets there with JJ+, AK.

He can have AA in 3 combinations (you block one A), KK in 3 combinations (you block one K), QQ and JJ in 6 combinations both and AK in 9 combinations. It's 27 combinations of hands.

Let's assume he folds JJ-QQ and AK to your 4-bet of 4.5$

So you are betting additional 4$ to win 2.3$ that's already in the pot in 21 of 27 times which equals 77% of the time.

On the other hand, if he continues (in 23% of the cases), you're risking to lose your entire stack of 10$ with the probability of 76,8%.

Summing up: 2.3$*0.77 - 10$*0.23*0.768 + 10*0.23*0.232 = 1,771 - 1,7664 + 0.5336 = 0,5382$ which means it's +EV. If he can 3bet with worse hands from time to time (everyone can) it's even more profitable. It doesn't include rake though.

I don't really know if these calculations are correct, I was just curious myself