A couple of ideas from when I was researching it. You can fill the bars with sand, as mentioned above, or silicon sealant. Not sure I would like that job
Heavier bar end weights seem to be a popular idea. I got some massively heavy ones that feel as if they weight half a kilo each, but they made no difference. As I said above, the problem wasn't the bike, it was my hands. I kept the weights when I sold the bike, and tried them on the new XTR for a week or so when I got it. No difference. I'd agree with Adioz - get them checked out by a medic.