Wethergig- probably weather rather than something to do with sheep.

Let's try The Scots Dictionary.

gig - a silly girl, a prostitute, a silly, flighty fellow, a trifler.

gig - anything that whirls, an ingenious artifice, a curiosity, a charm, a winnowing fan, a jig, a state of flurry.

So, a whirligig or toy windmill, punning on sexual laxity.

Grin - grind, war, wark (= work)

Clap - possibly the lid of the hopper which contains the grist.
Or perhaps the governor, though this would be a very early reference.
titter totter- bounce around.

Burning- fire was an ever- present hazard in mills, with the grindstones and underlubricated mechanisms producing heat, and plenty of combustible material around. The miller might need a lot of water quickly.

As for the meaning, you need little Scots to know they were at it - like the clappers.