Tony Clayton's website (the second of SuperDave's links) has a good compilation of British denominations with weights to the nearest 0.1 gram. If you want more accurate weights for these, or weights for other world coins, I'm not sure where to look. The Krause catalogues and their NumisMaster website have weights for precious metal coins but not base metal ones, except where there are catalogued varieties where the weight is a key difference.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis