This figure of speech means "through difficult and easy times," "steadfastly."

The expression is first seen in print in Chauncer's The Reeves Tale where, in the escapade of the clerk's horse, we read:

"And whan the hors was loos, he gan to goon Toward the fen ther wilde mares renne, Forth with "wi-he!" thurgh thikke and eek thurgh thenne."

But Spenser, in The Faerie Queene, suplies the best clue to the probable original meaning:

His tyreling Jade he fiersely froth did push Through Thicke and thin, both over banck and bush

That is, the expression is a metaphor with going through both thickets and thin (woods).