There's simply no way that you can convey to a company that they need to pay you twice as much as they did when they hired you 3 years ago. They simply won't believe it. Sadly, the only way is to demonstrate it for them by actually accepting a job somewhere else for twice the money.
The key is to remember that you're in this game for yourself first. It's nice to work for a good company with a good environment and a fun team, but at the end of the day it's not worth leaving tens of thousands of dollars on the table just to stay there.