Question about reverse equity in a tournament

Im not sure if its called reversed equity, but thats what it seems like. Say I have 99 heads up in a heads up sit n go and we know my opponent only raises pp's (22-aa). So my equity is 55% agaisnt his range meaning I have the best hand most of the time. Lets pretend blinds are 100-200 and he post the sb leaving him with 1400 and I post the bb leaving me with 1300. He raises as usual to 500 leaving him with 1000 and making the pot at 700 and gives me great pot odds with almost 2:1, plus I usually have the best hand. So technically its incorrect to fold with my hand agaisnt his range. So Now I re-raise all in for 1500. There is now 1800 in the pot and it cost him 1000 into 1800 . We know out opponent will fold every hand except tt jj qq kk and aa.. However if we raise hes only goin to call when he has us dominated. So 55% of the time we win a pot but dont win the tourney, but the other 45% of the time, we are dominated and will probably lose the tournament not cashingWhat is the correct move here and WHY. Thanks guys

P.S.

Also im happy to report I have started with $3.00 a friend gave me and rolled that up to $28.00 playing 1 cent 2 cent short/long handed ring, $1.20 & $2.25 1 table sit n gos, and $2.15 heads up sit n gos.

I don't know how you can ever have that solid a read on him. He's always folding AK/AQ/AJ? He never has any of those or any other two overs when he makes the initial raise (because him folding JT here is actually a good thing for you, for instance)?

Assuming everything you said is absolutely true, then just call the bet and shove over his flop bet no matter what comes, as after a c-bet he'll be committed to calling you.