I think there's going to be some differences between leaf spring/solid axle, versus independent. The importance of a level trailer.
As in that thread it was noted that -- in some instances -- some tandem axle trailers showed one tire of four taking a disproportionate amount of the load, it would behoove us to take the time to separate out the per wheel weights (not just across the trailer averages).
Floorplan is the obvious answer to the question. I think of the "classic" layout as placing the kitchen appliances, furnace and air-conditioner above the wheels, with maybe only the water heater out of the way. A center bath would better that arrangement, slightly, but it would seem to be the placement of the fresh water tank might be the most important consideration (under floor and between and barely ahead of the wheelwells).
Side-to-side, empty to loaded, will be, IMO, more a matter of what is packed as supplies and where. Canned goods/beverages being the killer (after serious toolboxes such as with yours truly. I won't mention my books although they are not at either end).
"Axle set" may be to one side or another, and not just "down" over the years; with any suspension type (past manufacturing mistakes).
So, back to layout: refrigerator across from kitchen counter/furnace/stove would seem to be a good minimum. Cabinetry materials and extent would dictate the rest. Propane and batteries seem almost universally tongue-mounted (or close to it), so that's a wash.
Owner additions would be the big thing. But how heavy are camping supplies carried in the trailer (for travel) that might be used elsewhere on arrival? A Dutch Oven collection and firewood plus bikes carried in the front "lounge" might well introduce a side-to-side imbalance (off the top of my head).
On my old trailer, the rear axle always wound up with more weight than the front (beam type). Didn't matter about FF-RR attitude in hitch height adjustments either. That trailer was flat light on the front (layout), and our additions didn't change things much.
As am now a single full-timer I'm looking forward to some weighings that will include wheel position numbers as I expect my load will not change much, and, hopefully, be of aid in choosing best tires.
1990 35' Silver Streak Sterling
; 9k GVWR.
2004 DODGE Cummins 305/555; 6-manual; 9k GVWR.
Hensley Arrow. 10-cpm solo, 18-cpm towing
Sold: Silver Streak Model 3411