The time weight multiplier doesn't always increase the winning amount.
Assume that the prize pool is 1 BTC and there are 100 winners.
If there was no time weight multiplier, each of the winners would get 0.01 BTC.
The time weight multiplier makes the profit of those who placed their bet early more than 0.01 BTC and those who placed their bet late less than 0.01 BTC.
Are you sure about this? Your example assumes every winner who placed a bet placed the exact same bet amount, which is a pretty big assumption to make. Anyway, I was under the impression the time weight multiplier always gave a boost to the final outcome odds, it just gives less of a boost to those who bet late.
If someone knows the formula freebitco.in uses to calculate the betting payouts, it would be greatly appreciated if they could post it.