Ceaselessly means without ever stopping. Rained ceaselessly, worked ceaselessly, campaigned ceaselessly.
It is admiring of effort and weary about weather, which is the whole range of the word. It is stronger than constantly and carries the sense that somebody wished it would stop.
1adverbceaselesslyWithout ever stopping.
“The volunteers worked ceaselessly through the night to rescue people from the flood.”
ceaselessly is a manner.
From ceaseless + -ly.
Etymology from Wiktionary, CC BY-SA