This looks like a copper massa from the Chola kingdom in Sri Lanka and southern India about 900-1300 AD. These are also called "octopus man" coins because of the appearance of the king in his robe.
Yes, there was considerable variation in coin weights in medieval India, though this is a rather large deviation. While very interesting to have in a collection, this is a relatively common type of coin, not highly valuable, and I'm not aware of fakes in this area. So my guess is that it is probably genuine.
The weight is high, the writing is not exactly correct (could be due to wear and/or different die engravers), and the coin is rounder than expected for a medieval hand-struck coin, but many "octopus coins" are relatively round. All together these factors raise some suspicion, but overall they do not convince me it is a fake.