so another hand, let me know if you like how i played it, or not

poker stars $25 NL

i have $20, opponent has $31.

I am in MP1 with 77, i limp (along with two other limpers)

Button raises it to $1.

I am the only caller.

The flop comes 4 7 4
i check, he checks, I was hoping he would follow through on a continuation bet..

The turn card is a 9, I thought and i decided to check again, he checks

i am 90% certain he has AK here

the river comes a K

no flush draws or straight draws. I decided I wanted to look like I was buying the pot, I bet double the pot (like $4) hoping he would raise, or at the very least call

Is this a bad way to play it? i was trying to make it look like I was overbetting the pot. He called with AK

how would you have played this?