Just like in the last Willie installment, Willie is using current meteorological conditions as a justification to go for the hooch.
Peart - lively
Fitten' for to lower - I'm not exactly sure, but I think he's saying it's too windy to lower the sails.
Slug of plush - the "slug of" part of this expression is still in common use - the "plush" part took me some googling to find, but I did track it down finally to The Yellow Admiral by Patrick O'Brian. I guessed that the term Plush might have to do with the Dorset village of that name - Dorset being an English county with a sea coast and so perhaps involved in the rum trade. Regular readers of the blog also know that Dorset is the home of Doollee.com creator Julian Oddy.
I wasn't able to verify my hunch about the Dorset village but at least I did get a definition of "plush":
Harding came in, bringing the sun with him. 'Forgive me for bursting upon you like this, sir, but I have had such a pleasing letter - my wife has just inherited a little estate in Dorset from a distant cousin: it lies between Plush and Folly. I am to be squire of Plush!'
'Give you joy with all my heart,' said Jack, shaking his hand. 'We shall be neighbours - my son is at school there, Mr Randall's school. How happy my wife and I will be. But I am afraid that I must warn you that Plush often leads to Folly.'
'Why, yes, sir...' began Harding, somewhat staggered: but then he caught the nature of Captain Aubrey's witticism (perhaps the best thing Jack had ever said) which depended on a knowledge of the fact that when grog was served out the ordinary members of each mess of seamen received slightly less than the regular measure: by ancient custom, the amount of grog left, which was called plush, belonged to the cook of the mess; and unless he had a good head for rum, this often led him to commit a foolish action.
There is indeed a place in Dorset called Folly, in Piddletrenthide, to be precise, although it must be tiny, it doesn't get named on the Google map, while Plush, which is indeed near Folly, does.
I suspect that the joke about Plush leading to Folly was huuuuge in Dorset. Ah Dorset, the county of piquant place-names as you can see in this Wiki list, like Wool, Melbury Bubb, and Ryme Intrinseca. Folly is so small it isn't even listed here. But then again, neither is Wainscotting.