Click
http://www.bollixed.net/bollixed/thesaurus.shtml
and a link will take you to a page with some 200 words/phrases - including your own - meaning 'drunk'. If you study the list, you'll see that hardly
any of them is susceptible to rational explanation. Nor is it very likely that an actual source will ever be isolated. 'As drunk as a rat' is centuries old, but why/where/when that became the modern 'rat-bottomed' - except that it isn't 'bottomed', of course - I don't expect we'll ever know!