To give a direct answer to your question - shoving here is just foolhardy. 2 pair is a very average hand at showdown, especially staring at a possible completed straight, a flush draw, and maybe even a set. Honestly, did you even slow down to FULLY consider what he might be calling your check raise with? Then the T comes to make the straight so you shove?!?!?! You figure he's on a flush draw?!?! What if he has QJd? Very possible holding to call you with and go to the turn (among others).
The general rule is - Small hand? Keep it a small pot. Big hand? Make it a big pot. Two pair is not a big hand.
The question is why are you shoving here? What were you wanting to happen that you would escalate the risk factor to twice the size of the pot on an average hand? That's not playing poker as much as it's shooting craps or spinning the roulette
wheel. If he has you beat or draws out on you then you screwed yourself. If he doesn't draw out (as in this case) you are pricing him out of the hand (but in these micro's they won't go away like they should all the time). Most of the results of a shove here are bad for you. The best you can hope for is he calls and misses a draw - but what if he has a set? What if he just folds? Risk your stack to make .60 cents? Not a great investment.