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Ahoy, DW. Thanks for all the suggestions. GULLIVER already makes use of square root of mass in many places: in target knockback distance, in weight-based damage (drop kick, stamp attack, trampling, weighted blows), exposure hazards, collision damage, terminal velocity, and maybe more. Putting a name on this and pre-calculating it are things I should have thought of from the start. Good idea!
So, we have a stat called MR, which is 12 for a typical human. What can we do with it?
Falls and slams: As you suggest, let it replace HP for damage purposes under 4e rules. Sounds perfect. I know the current use of HP here has been unsatisfactory for many.
Sacrifice takedown: Your suggestion sounds good on the surface. We need to take a look at the basic idea of adding a portion of MR to ST:
GULLIVER uses the following general method for combining weight and ST: (some multiple of) mass + (some multiple of) Load ST. My reason for using Load ST, not regular ST, in Contests etc. was so this would work well: Load ST is the "correct" stat for direct comparisons to weight. I believe this is a sound method, so want to pit your suggestion against it.
Your suggestion under 4e essentially replaces that with this method: (some multiple of) square root of mass + (some multiple of) ST. The latter equates to square root of Load ST. So we've got the same approaches, with yours using the square root of each item instead. The specific probabilities generated for a given case will change, but unless there's some flaw I don't see, it sounds robust to me; as long as we're not taking the square root of one and not the other, I like it. So let's assume it's a good method for now, and run on to other ideas:
Takedown: I think the method you suggest doesn't run into big problems. And given too little time to think these days, I'll continue to think so until someone tells me otherwise.
Pinning: There are two actions here, making the pin and maintaining it. For making the pin, in GULLIVER I decided to use the exact same rules as takedowns (without, obviously, options like sacrifices): two fighters rolling around to get on top, with a bonus going to the heavier (whether the heavier is the one trying to make the pin or avoid it).
For breaking free vs maintaining a pin, though, I thought it makes sense for only the "top" (maintaining) fighter to get a weight bonus, and that based on absolute (not relative) weight. Further, I'm not sure it's necessary to compare MR to ST as you suggest; if A's ST is high, and B's MR bonus is low, then A is already well-equipped to shrug off B's weight without further adjustment.
So sticking with the general flow of my old rules, I'd have making a pin work per your suggestion for takedowns, and maintaining a pin work by giving the pinner a ST bonus of, say, MR/3 or even MR/2.
Is there an argument I'm missing for changing the approach?
Weight-based damage bonuses: Right, they'd work nicely as you suggest.
More applications:
Natural encumbrance: Instead of a rule comparing BL (the 4e incarnation of Load ST) to mass, why not plain ST and MR? The level cutoffs for a natural encumbrance chart will have to be changed, but MR / ST is perfectly good as the core determinant of mobility. One issue is that you'd have to keep natural encumbrance separate from item encumbrance, assuming you want to track items using a simple running total of their weight and not include their mass into the calculator-loving extraction of MR. That leads to a long discussion of how to best work natural encumbrance, but for now let me note that MR / ST may make for a nice new base.
Knockback: I don't have my books on me, and couldn't tell you off-hand what the rule is for mass and KB in 4e. But if an alternative rule is called for (and I don't know that it is), MR (or a multiple thereof) may make a great divisor for KB purposes. It'd be right in line with existing GULLIVER rules.
Final note: The rules do, as you suggest, give large creatures substantial bonuses that GURPS does not. Yet on the other hand, GULLIVER gives them similar bonuses, and some of those based on full weight, not its square root. So the MR-based suggestion, in some cases, should strike a nice middle ground between the two, giving large creatures bonuses that are substantial yet don't scale wildly with mass. We'll have to check specific examples, but it sounds promising so far. This is definitely good fodder for the GULLIVER update (which, for any passers-by, is even getting an open start at http://www.gamesdiner.com/node/80 ).