drthos

I agree that the ulnar nerve is the likely culprit. But most of the ulnar nerve runs along the medial side of the wrist (the side closest to the pinky,) and along the medial portion of the palm, not up the middle of the palm (that's the median nerve.) The ulnar nerve does cross over to the lateral side, but at that point it's not really vulnerable to compression.

The most likely time to be compressing the ulnar nerve is when you're riding with your hands on the hoods, since the medial & proximal portion of your hand is usually resting on the top of the handlebars. Your gloves probably aren't implicated, unless they're very tight at the wrist (and even then, it's hard to imagine, since the nerve is protected by tendons & the wrist bones at that level.)

This may be a tricky problem to avoid competely on long rides, but try to avoid resting on the medial side of the palm or the medial aspect of the wrist...

If the weakness persists, you'll definitely want to see someone (preferably a neurologist,) to try to specifically localize the problem, which will help in coming up with a strategy for preventing it from getting worse.