Holding down the CTRL key in right clicking in the PuTTY terminal window will bring up a menu with a good few options on it, one of them is full screen.

This is a handy wee feature because if you are doing anything that will take more than a couple of minutes having a small window can quickly become distracting (all the windows behind it become background noise) and of course now you have more screen real estate for things like VI to play with.

To come out of full screen mode CTRL and right click again and click full screen again.