I'm a long way from a battery expert (don't want to be one anyway ... it's more fun just to use them for happy camping), but here's a couple of very, very general comments regarding the "weight" of a lead acid (liquid or AGM) battery:
1. For any given physical case size and nominal voltage of a lead acid battery ... probably more weight means it has more energy storage capacity.
2. If physical case size is no object, for any given nominal voltage of a lead acid battery ... probably more weight means it will have both more energy storage capacity and, assuming it is properly taken care of, a longer lifetime.
I'm sure someone can chime is and say it much more accurately than I did.
P.S. In my situation, I wanted the most capacity - hence largest case size of the right shape - that I could fit two-of into our rig's intended stock battery storage compartment, not corrode the area, and take zero maintenance. This meant two size Group 31 AGM 12 volters or one size 8D AGM 12 volter. A single 8D was way too heavy for me to man-handle into and out of the battery compartment. Golf cart shaped batteries would be too tall while at the same time wasting volume due to their base width and/or length dimensions. About my only choice was two Group 31 AGM 12 volt deep cycle batteries that were the heaviest I could find with both a stellar reputation and the proper specified float voltage value. Lifeline AGM batteries offered the most capacity per their size and shape (and therefore were the heaviest for their size and shape) - but their specified float voltage value was not a correct match to my RV converter's nominal output voltage day-in day-out.