끼다 can be a few things, but in this case it's "to be hanging" or something along those lines. So, "In the sky, clouds are hanging". It's in past tense because they were already "hung" there.

Excellent question!

This is 끼다 hanging + 었 past tense (for state) + 어 casual talking. 하늘에 구름이 끼다 is not for talking, it is for announcing statement like forecast.