I’ve also seen alternatives to the “biggest weakness” question.” But I’ve never loved any of them. So I’ll throw one alternative out there.
Instead of asking people their biggest weakness, and having them say, “my biggest weakness is that I care too much,” how about asking this:
From what you know of the job, what do you think would be your biggest challenge on the job, or the thing you will most need to learn as you get up to speed?
That might get you a good answer, a job-related answer — though as you know from my previous posts, I’m skeptical of people who answer, “Nothing!”