Perusing Webster's Unabridged Dictionary is one of those things that I honestly enjoy. I also love thesauruses. Don't judge me. That's why I can tell you that there is more than half a page in my door-stop-sized Webster's devoted to the word "purchase" with at least a dozen varied meanings given. Our concern here, of course, is the vocabulary of freebooters in particular and sailors in general and in that sense a couple of etymologies stand head and shoulders above the rest.
To the flibustes and boucaniers of old Tortuga, purchase was defined as all goods and cash obtained during a raid, by sea or land. The ancestor of that usage is undoubtedly the French word pourchasser meaning to pursue. Of course, most people know the piratical bon mot about no purchase no pay. I've a hunch that came down to us from guys like Francois L'Olonnais via Henry Morgan and his ilk. Find a prize or go hungry, mate.
In the over-arching nautical sense, purchase is much harder to pin down. The word started out meaning any mechanism which increases the force applied to an object. In this sense "a purchase" might be a block-and-tackle, pulley or capstan. "Light along and bring us a purchase to pull this tortoise aboard."
As the English language evolved, this definition morphed into one of the ways we use the word now. As Webster puts it: a fast hold applied to move something mechanically or to keep from slipping.
From what I can tell, the buccaneer use of the word is entirely of French origin, while the other two seem to be English speaking inventions. That's just the way I'm seeing it, though. If you've another thought on the matter, chime in on the comments.
Happy Saturday, Brethren. Enjoy!