Bad push??

[PokerGoblin]

8 handed live freeze out. NLHE $20 buy in plus one $20 add on. 2k chips to start, 2k add on. Top two get paid. All remaining players have taken the add on already. Blinds are 300 and 600.

Approximate stacks are:
Me: 5800
Seat 2: 7500
Seat 3: 1200
Seat 4: 3300

The big stack has been min raising pretty much every hand. I have suspicion he has been getting hit with the deck, but undoubtedly has been stealing pots. He has shown down some legitamate preflop raising hands. He is also prone to calling all in raises preflop with less than stellar hands.

On to the hand:

Four handed I am dealt A-7o in the SB. Folds to me, I complete, BB min raises (as I expect) and I push.

Standard play?

If you think this is a bad play, how strong do you have to be to make this play, knowing you will likely be called by a wide variety of hands? Including A-4 and higher, K-9, k-10, Q-10, and Q-J are all hands he will likely play with. He will likely also call with ANY pocket pair.

Thoughts?

PG