I've played many games and there are basically 3 ways to counter heavy cruisers:
1) More Heavy cruisers
2) Heavy cruisers and bombers
3) Long Range Frigates (or Illums) and bombers
4) A ton of Illuminators
A couple of notes regarding this conclusion:
http://spreadsheets.google.com/pub?key=p7xc_snd9Cc-6o2UwvPEWUg&gid=1
Go to the link to see that there are only 2 ship types other than cap ships and more heavy cruisers that do 75% or more of their damage or more to heavy cruisers: Those would be long range frigates (in this case including the advent illuminator) and bombers.
Though bombers would do the most damage statistically to heavy cruisers due to their insane dps to begin with, carriers will get pwned by heavy cruisers because they tend to be relatively slow, and heavy cruisers chew them up like tissue paper.
A Quick Note About Carriers:
Carriers are great, but because their fighters tend to target w/e they feel like (though it is typically what they are most effective against), it is always best to group all of your fighters to ctrl#6 and bombers to ctrl#7 (or some such grouping). Doing this allows you to micro your bombers to all attack one heavy cruiser at a time. This "Everyone attack one ship at a time" strategy is particularly effective against larger ships like heavy cruisers, where the damage lost to "overkill" is minimized.
Critical Note:
I mean to make a posting on how the game tactics are affected by the fact that ships cannot explicitly target what they are not "chasing", but, partly because of this fact, because of the time it would take the heavy cruisers to catch up with the carriers, and critically because of the carrier group's ability to "scatter", it is not worth chasing carriers unless the other ships in the system are not threatening to your fleet.
Therefore, the best tactic would be to use bombers, but to prevent their carriers from "being chewed up like tissue paper". To do this, another ship type is required to prevent the heavy cruiser player from "chasing" the bombers around the system.
There are two types of ships which can do this effectively:
#1: More heavy cruisers work well at this, because they do high dps to heavy cruisers
#2: Long range frigates (including the illuminator), which, while they do less damage to heavy cruisers than more heavy cruisers, have much longer range allowing them to chase the heavy cruisers and take them down very fast if they chose to go after the carriers, and, most importantly, are much easier to have many of by the time a player gets a lot of heavy cruisers.
Therefore, I have found counter #3 at the beginning of this post to be the best way to deal with heavy cruisers, because I tend to get many long range frigates to begin with, no matter what race I am playing.
Basically, the build order for these counters is thus:
1) If you already have a fleet of long range frigates, then start pumping carriers with bombers.
2) If you do not already have a fleet of long range frigates, get heavy cruisers, because splitting production between long range frigates/heavy cruisers and carriers will typically not produce results fast enough to be an effective counter.
3) If you are playing as advent and do not have a fleet of illuminators already, it is actually plausible to start pumping nothing but illuminators to take out the heavy cruisers because they still do 100% of their damage to heavy cruisers and are pretty good, especially against the short range heavy cruisers.
CRITICAL FINAL NOTE:
Though all of these strategies work in the general case against heavy cruisers, the ones that don't involve getting heavy cruisers all have one weakness, flak frigates/sentinels/(and most crucially) defense vessels. These three anti-light frigate ships will obliterate your long range frigates while at the same time countering bombers relatively well. Also, Carriers with fighters counter long range frigates especially well, and also counter bombers for obvious reasons.
And what are the counters to flak frigates/sentinels/defense vessels and carriers?
#1: NO GOOD Light Assault Frigates NO GOOD (ie: Skirmishers/Cobalts/Deciples)
THESE ARE NO GOOD.
Light Frigates will (again like tissue paper) be torn apart by your opponents heavy cruisers.
#2: Heavy Cruisers THESE ARE YOUR BEST BET
Essentially, and many of you may have noticed this, as soon as one player starts massing heavy cruisers, everyone needs to start getting them. Bombers/(Rediculous Cap ship comos that fall apart when fleets get large due to the "everyone target the cap ship!" effect)/ long range frigates all work well against the heavy cruisers, but once your opponent starts countering your fleet types you will have to make heavy cruisers yourself.
My Conclusion:
Once you get your anti-heavy cruiser fleet
Upgrade the prototype research for your own heavy cruisers so that you can make them as soon as your opponent gets smart.