As the ASL player base ages this will be a common problem. It would be nice if MMP would do a complete graphic re-design of ASL. But I doubt that they would be able to justify the cost.
Look at Combat Commander as an example of a more modern graphic design in a tactical game. Personally I don't care much for the card driven gameplay of CC but I admire the graphics. The basic unit counters are 5/8" rather than 1/2" and have a crisp graphic style that makes them easy to read. And the maps have large hexes. Of course if you give the standard ASL map hexes as large as Combat Commander it would double their length and width and make their overall area 4 times larger.
Maybe one solution for you would be to get one of those huge Sherlock Holmes style magnifying glasses and use it to examine the ASL playing field.
I think that the newer counters from MMP supposedly are a larger font. I haven't seen them yet though. Also, how big can it be? The counter is still little.
Playing on VASL may help as well, though I'm not sure that you can enlarge this yet.