There seems to be some disagreement even among the so called experts on this one. On average it is the Polar Bear hands down with an average weight of between 900 and 1500 pounds, the largest ever recorded however was only 2210 pounds. The Brown Bear or Grizzly has an average weight of between 500 and 900 pounds, the largest ever recorded weighed in at 2500+ pounds. So, you decide, and I hope the bet wasn't for any serious money because the answer is pretty ambiguous. See the link.
http://www.loc.gov/rr/scitech/mysteries/bear.html