Pidge may be missing conversational details, but Wash sure isn't. Her trailing off and wiping her eyes fits one of a very short list of options; the thing is, making a big deal of it will probably make everything worse.

So he puts a hand on her shoulder and does the best he can. "Hey, go get some rest. I'll grab you some dinner later." If he can't address what he's pretty sure is the real problem, he might as well get the next one over.