Translation:The girl likes the skirt, despite the color.
To go deep into "apesar", you can think of it as "a + pesar" (to weight - to burden).
Thinking far beyound, it would be: The girl likes the skirt, although the color is a burden. (That's not an acceptable translation, I'm just adding ideas onto it)
There's no word in english to suffice that exaclty, so you have to chose the one that fits best, in that case, despite is a good choice.