What is the average size of all tiles for a US state?

To get an estimate of the number of tiles you need to cover a state, go to map.geofabrik.de and activate the "tile coordinates" overlay (from the layer switcher in the top right corner of the map). Zoom in on the state you're interested in. You'll get something like this:

So, Colorado for example has about one and half tiles on zoom level 6. The number of tiles quadruples for each zoom level, so you are looking at...

• 1.5 tiles on z6
• 6 tiles on z7
• 24 tiles on z8
• 96 on z9
• 400 on z10
• 1600 on z11
• 6400 on z12
• 25k on z13
• 100k on z14
• 400k on z15

making a total of roughly 500k tiles. Now the average size of tiles is a tricky thing, it varies between zoom levels. But if your scenario includes tiles on higher zoom levels then the average size is surprisingly small - something like 2 kB. Tiles can easily reach 50kB and more but on high zooms, most of Colorado will likely be almost empty and the empty ones dominate the few large inner-city tiles. (And, tile count wise, the higher zoom levels dominate the lower ones.)

So the answer to your question is that for a state the size of Colorado and up to z15, you're probably looking at 2 kB * 500k tiles = 1 GB of tile storage.