I lean towards preferring a lighter tire weight over a heavier tire weight.
My Falken AT3W's were P metric Standard Load (SL) - stock size 265/70R17
46.5lbs each (31.7 inches tall).
If you look at the Specs of the C load 275 Wildpeak AT3. You'll see that they weigh
57.1lbs each (32.4inches tall).
https://www.falkentire.com/tires/light-truck-suv-cuv-tires/wildpeaka/t3w-tire
My new LT285/70R17 E Rated Yoko Mud Terrains weigh
58.2lbs each (32.9 inches tall)
GEOLANDAR M/T(R) G003 | Yokohama Tire
Compare that against Falken E rated LT285/70R17 MT's at
63.3lbs each (32.9 inches tall)
https://www.falkentire.com/tires/light-truck-suv-cuv-tires/wildpeak-m/t-tire-0
Or Falken Wildpeak AT3 E Rated LT285/70R17 at
58.9lbs each (32.9 inches tall).
https://www.falkentire.com/tires/light-truck-suv-cuv-tires/wildpeaka/t3w-tire
You might run your own comparison for weights of 275 Falkens vs the competition. Above is comparison going to a taller / heavier / mud terrain tire.
If you are in a place that gets a lot snow, IMHO, an AT tire makes more sense than a MT tire. Where I live, we get maybe 1 good snowfall a year, and it's gone in a week or less.