Q From D Biddulph: Have you any idea about the origin of to bear up? (It’s definitely nautical and something to do with ship direction to the wind.)
A It’s an ancient phrase, which has been used in various senses, often literally to carry something up, or to be carried up by some force or action (“he was borne up by the force of the explosion”). The sense you mean, of staying cheerful in the face of adversity, could conceivably be connected with the sea. In its sailing ship sense, to bear up means to steer the ship more closely into the wind, a more difficult and uncomfortable thing to do than the opposite, to bear off. But the link between the sailing sense and the figurative one isn’t particularly close, and it’s conceivable that it actually refers to bearing one’s troubles, but in an elevated way that rises above the discomfort, the opposite of feeling down (though to bear down has quite another meaning, such are the peculiarities of English verbs).