I'm not speaking for Weird Al, I've no idea what his thoughts on the subject are, even if I did, I don't think I'd do that, and I'm not speaking for anyone else.
But if it were I making the decision of whether to produce and publish a parody of "We Are the World," I'd pass.
Why? Because there are some songs whose message shouldn't be interfered with in any way, or corrupted if you will. This is one of them. It appears that the humanitarian efforts, which were the whole reason for the song in the first place, were and continue to be successful and have saved many lives, not only in Africa but in the USA.
Just speaking for myself, I don't see anything to be made fun of here. And I'm not trying to be a killjoy. I'm not speaking for Weird Al, but I am saying that I think it's possible that not wanting to be thought of as someone who interferes with this kind of charity might have something to do with not producing a parody of it.