From Longman Dictionary of Contemporary Englishheavy sky/cloudsheavy sky/cloudsWEATHERclouds that look dark and grey as though it will soon rain → heavy
Examples from the Corpus
heavy sky/clouds• Looking northwards towards the end of the dale, she frowned to see the accumulation of heavy clouds above the moors.• Under dark, heavy clouds, I returned to the den on the river.• But towards morning heavy clouds spread across.• While they slept, heavy clouds swirled over the valley in massed ranks and the snow began to fall.• The heavy clouds that had gathered about the summit of Mont Blanc boiled from within.• Dark heavy clouds were crawling across the sky, blotting out the stars. 