Searching a Project Gutenberg etext of Jude the Obscure, I found a dozen other instances of "med", such as these:
"Now don't you interrupt, my boy. Never interrupt your senyers. Move the fore hoss aside, Bobby; here's som'at coming… You must mind that I be a-talking of the college life. 'Em lives on a lofty level; there's no gainsaying it, though I myself med not think much of 'em. As we be here in our bodies on this high ground, so be they in their minds—noble-minded men enough, no doubt—some on 'em—able to earn hundreds by thinking out loud. And some on 'em be strong young fellows that can earn a'most as much in silver cups. As for music, there's beautiful music everywhere in Christminster. You med be religious, or you med not, but you can't help striking in your homely note with the rest. And there's a street in the place—the main street—that ha'n't another like it in the world. I should think I did know a little about Christminster!"
It seems clear that "med" represents a dialectal pronunciation of "might".