Tried a set of 225/45x15 Avons last season, would describe thus:
1) 225/45 size is a cantilever sidewall design, which makes them very heavy . Approx 6 pounds per tire more than a 205/50x15 Hoosier or Kumho. All of that is extra rotating mass and unsprung weight - you can do the math.
2) Compound seems pretty hard - they wear like iron, but correspondingly not very sticky.
So, if you're looking for a hard compound tire (for very abrasive track, or enduro), you might like it. I'd stay away from sizes that use the cantilever sidewall design. The Avon 205/50x15 is not cantilevered and would be similar in weight to the tires I mentioned above. Another Miata racer in this area is using them and seems to like them.
I'm using Kumho 710's this season, and like them a lot better than the Avons so far.
FWIW the Avon's came in 2 tread compounds. The original were long wearing and not so sticky. the second compound was like R-a or something was supposed to be softer. Saw them on lots of novice cars a year or 2 ago and now nobody seems to run them.....