LeadSled - I'm not sure about a 'rule', but the principle is sane - according to Mr Newton, F=ma (and therefore a = F/m)
So as M gets bigger, the same force will produce a smaller A (or G loading) - the aircraft is somewhat less sensitive to gusts. Last time I checked, the POH for the oh-so-common Cessna 172 listed two Va values, one for MGW, and one for very light weight. I don't believe there is a specific turbulence penetration speed, Vno around 120something, Va 104(?), so Va is/was generally taken as a safe turbulence speed, at least as I was taught. (Caveat I've not flown a 172 for ages, hence being a bit vague)
Also of course as the a/c gets heavier, there's a practical limit to how much acceleration that the wing can produce without stalling - not that that's a particularly useful method of turbulence avoidance, and all of this is ignoring any secondary effects, other than immediate acceleration.
Ultralights - in my experience of the Robin, yes, it's easy to buffet the roll off the top, however the problem is more likely to be one of reaching the top somewhere around, or even a bit below the level flight stall speed. Certainly you're unlikely to be capable of getting 4G. For a straight loop, that's less of a problem as you tend to float it over around 0G, but rolling off the top it's pretty easy to roll straight into a buffet / stall etc. Been a while since I aerobatted one, but I seem to recall adding 20kts to the entry for a roll-off or avalanche.