>>he might not stay long. He feels awkward when he's there, but like you said, he lets her know he cares and she's not really 'alone'.

That sounds very good. If he can only stay a short time that is OK. He has to know his own limits first. Trying to remember that the awkwardness is due to depression and is not personal may help.

IMO it is OK if he thinks he is overextending himself to cut back for his own safety/health. I guess like almost everything in life, the solution is finding the right balance.