2 limpers, push from BB with a pair of 4's?

[45suited]

Down to 6 handed, I'm BB. No SB this hand. Relevant players:

UTG t2100 (chip leader) calls 200
MP t965 calls
BB (hero) t820 after posting BB 4c4s

I pushed. I felt like UTG chip leader (who got all his chips with aces early on) wouldn't want to risk his lead with a marginal hand and that if MP called with two overs, that would be okay. Is this too aggressive or standard play?

Anyone else close their eyes, hope for the best and push here?