Comparing tire weights in a given size is problematic in some sizes because either that size isn't available in all tire brands being compared, or isn't available in the same load rating.
However, in an effort to determine whether Cooper AT3 or BFG AT is heavier (in same size and same load rating), I looked at a few sizes. Of the sizes I looked at so far, only 30x9.5R15C offers apples to apples comparison of same size and load rating.
Note that the Cooper AT3 is slightly heavier than the BFG AT when comparing same size and load rating. See 30x9.5R15C section below. I don't think Cooper AT3 is less tough than BFG AT. My best guess is their toughness is comparable, and close enough to be a non issue.
Also note: Cooper AT3 30x9.5R15 is 29.3 tall, not 29.2 tall was previously posted.
I did not compare weights of size 31x10.5R15C because the height/size differences are substantial between brands in that size.
In 30x9.5R15 and 265/75R16C the height/size differences are insignificant, IMO.
i.e. - all brands compared are very nearly the same actual size.
Unfortunately in 265/75R16 not all brands are available in load C for comparing weights of C to C.
30x9.5R15 load C
Cooper AT3 29.3 tall, 39
BFG AT 29.5 tall, 37
Toyo AT2 29.5 tall, 37 lbs
Hankook ATM 29.5 tall, 40 lbs
265/75R16 load C
Cooper AT3 31.6 tall, 46 lbs
BFG AT unavailable this size load C
Toyo AT2 31.7 tall, 45 lbs
Hankook ATM unavailable this size load C
One issue not discussed is availability of size you want in a load rating you want. Sometimes you take what's available, even if it wasn't your first choice of brand.
Lack of availability can make valid weight comparisons impossible for some tires in some sizes/load ratings.
However, I can say that for 30x9.5R15C the Cooper weighs slightly more than the BFG AT. So the earlier statement that BFG AT is probably tougher because it's heavier seems doubtful to me when comparing tires of same size and load rating.
Ultimately though, if you're after a certain actual size in a certain actual load rating, you've limited your brand choices. That's OK though, as long as there's still something available that you want.
These issues recently led me to buy 16 x 7 stock Icon wheels in case I ever want to run a 245/75R16C tire.
I like Cooper AT3 and Hercules AT2, but I agree they run significantly small in 31x10.5R15. That is an advantage for anyone with fitment/clearance concerns, but is a disadvantage for everyone else. So I understand why Silvanus doesn't want a Cooper AT3 or Hercules AT2 in 31x10.5R15.
In the 30x9.5R15 I am currently running, the Cooper AT3 and Hercules AT2 run in
significantly smaller than most brands (0.2" shorter means 0.1" lower diff, which is insignificant). So I'm good with those tires in 30x9.5R15C.
In 245/75R16C, the Cooper AT3 and Hercules AT2 run exactly the same size
as other brands I've looked at. They are all 30.5 tall in 245. Since I like Cooper AT3 and Hercules AT2, but don't want them signifigantly short in whatever size I run, I'm currently running 30x9.5R15C, and if I have enough lift, I might switch to 245R75R16C in future.
I never considered AT3 31x10.5R15 partly because to short (30.2), and mostly because I prefer narrower tires. I wonder if a Cooper AT3 31x10.5R15 might fit a stock XJ? With fender trimming maybe?