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What does check-raising all-in on the flop accomplish here?

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Gives you some chance of folding a better hand (TT, AJ, AQ) and if you are called it guarantees you (1) see the river, (2) win the most when you hit, and (3) eliminate an opponent when you hit.

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I'm not sure I buy a tight player having TT or AQ (much less AJ) here. Doesn't TT check behind on the flop, too?

Anyway, I don't think the chance of folding the occasional better hand is worth giving away chips to the more likely hands that you're well behind and will call the push.