"좋아해요" is a transitive verb meaning it always needs an object with the object markers 을,를, on the other hand, "좋아요" is an adjective, it doesn't need objects, instead, it needs subjects with the subject markers 은/는/이/가.
e.g.
I like apples.
= 저는 사과+를 좋아해요(O), 저는 사과를 좋아요(X)
= 저는 사과+가 좋아요(O), 저는 사과가 좋아해요.(X)
\^o^/