좋아요?, 좋아해요? have same meaning, but usage is a little bit different.
ex) I like you. --> 나는 당신'을' '좋아해요'. 나는 당신'이' '좋아요'.
Do you like me? --> 당신은 나'를' '좋아해요'? 당신은 내'가' '좋아요'?
We use '좋아해요' with the objective, in this case, need to use the post position(조사) '을, 를'
'좋아요' is used with a complement, in this case, need to use the postposition '이' '가'
I hope this answer would be helpful for you.