Unity2D - 16x16 Tiles show up in-game super small

I am working on a 2D Adventure/Shooting game using Unity2D. I downloaded a 16x16 asset pack, you can find it here. I got everything sliced correctly, but when I placed it on the grid it shows up really small and has a big grey border around it. I have already tried sizing down the grid cell size, but when I change it to a small value (eg. 0.1x0.1) it lags a lot and is not really optimal for my game. How should I solve this?

Here's a picture:

 

You probably want to find the sprites in the Project tab, select them and set the Pixels Per Unit to a smaller number. This number defines how many pixels should be in one Unity unit.

 

Thanks! I'll try it out.