The support cruisers have abilities to help fight HCs.  Advent Repulse pretty much renders HC's useless while you kill them with Illums.  Hoshikos with Demo Bots are useful if you have enough Hoshikos to muck with the HC's while your other ships are killing them. 

Vasari used to be able to use Subverters, but they run out of juice fast now and don't give nearly as much bang for their buck....the HC's won't die fast enough and will just kill the Subverters most likely.  Not that a Vasari player is going to have Subverters in time to stop a fast rush.  To be honest, I've done pretty well with large numbers of upgraded Assailants and eating up the HC's with Nano from my Egg in pure rush situations where the other guy hasn't had time to mass large numbers of HC's yet.

Bottom line, if the other guy has an all HC fleet, you probably should have a large quantity of bombers, and if he makes fighters to shoot down your bombers, you make flak to shoot down his fighters.  If you get hit by tons of HC's and all you have is LF & LRM, you are probably not going to win.  There are only so many ships counters -- HC's are countered by Bombers, Support Cruisers, and your own HC's.

Cykur and Top pretty much nailed it on the nose.

Best thing about going HC's is there's only one thing out there designed to counter it: Bombers

If you're fighting HC's, your options are in order of effectiveness:

1. Bombers. This should be your first option, HOWEVER in late game scenarios these probably won't do it alone. When I go HC, I also get fighters to kill off bombers and hoshikos/guardians/overseers to keep the rest of my stuff alive. Bombers are the quick and easy answer in early game scenarios with a rusher. Late game with a guy who has a massive eco? Nope.

2. Heavy Cruisers. HC's get a bonus attacking themselves as odd as that sounds. TEC and Advent have roughly on par HC's. Kodiaks are better early. Destras are better late game. Enforcers kinda suck tbh.

3. Long Range Frigate. This one is kinda counter-intuative, however, I can tell you that you can overwhelm an HC user if you are quick enough to outproduce his ship production. This probably won't work once he has say 6-10 kodies out and about, but if you want to get aggressive, you can expand quickly and effectively towards him and strip him off any planets to expand to. It's an option, but of the three mentioned here, it's probably the worst one.

not to mention that's a great counter to a lot of things