Hello! Offering to the community a short script to "embiggen" the go stones, currently works correctly only on 19x19, and get strange results on the smaller boards.

Anyhow if anyone wants the stones to nearly touch, here it is:
javascript:(function(){ var a = document.getElementsByTagName('piece'); for(var i = 0; i < a.length; i++) a[i].style.width = '5.7%';})()

Disclaimer:
It only works for the currently available stones, so it kinda works for correspondence games while you ponder your next move on the board. Every move that happens after applying the script won't take the redefined size, so will resume to be placed with a smaller size. If you scroll up and down the move list, results may vary.

If you want to fiddle with the script and improve / tweak it:
The value to alter if you want to experiment yourself is that 5.7% near the end.
It might be possible to edit that width to make it work on the other sizes too, but I leave that as an exercise to the reader.