The base sizes do not vary a whole lot, height does. When I was deciding on batteries for my new trailer size was a big issue, but I wanted plenty of capacity as I will be eventually adding Solar and an Inverter. So went with 4 Lifeline 6v AGM Batteries, quite pricey. They are almost 100 pounds each so installation planning must account for the weight. This setup should give me 600Ah at 12V. I do have concerns about being able to charge them adequately till I get Solar, but he generator is being installed right now.
I've heard that generally the better the battery the heavier the battery, as the plates are thicker.
As far as tongue weight, you shouldn't be so close to your limit that a few pound difference is much of a factor.