The 0560 series actually weighs in at 6.4oz. A while back they stopped milling the Ti slab which increased weight.
As for OP's question, I would go for the 0562. The materials you get are better overall and ELMAX is generally better than D2. You already mentioned you have an ESEE 3 and 6, so unless you plan on putting those to the side while you batton with your folder, I can't see any reason you would need something as heavy as the Adamas. Also, given the higher grind of the 0562 it will slice better. And contrary to what Whitty posted, the stock thickness on the 0562 is the same most other ZT's (0.160") which is also the same as the Adamas.
Though my opinion may be slightly biased because I love me some ZT's.