How much of a difference from the proper weight of a coin before you can start to suspect that it was minted on a different plancet ?

Each type of coin has it "specification weight" with that "specification weight" there is also a "tolerance", tolerance is going to be a variable rage of +/- from the specification weight. if a coin falls within the tolerance of spec, it's nothing special and an acceptable variance in the weight for the mint to use it. You have to know the weight of the coin in question first, then these things before going further to determine anything really. What does the coin weigh? What should the coin weigh normally? What is the tolerance range for the coin?

Out of tolerance weight would be much more indicative of a thin or thick planchet, rather than wrong planchet.

I don't know about indicative, but a rolled thick or thin planchet would be the vastly more likely reason for it being out of tolerance while off metal or wrong planchet would be a super long shot, and neither are very common to happen to begin with. I see more "missing clad layer" which will make it light, than it being light from any other reason and this only affects dimes and quarters half dollars and ikes since the late 1960s.

You also need to be aware of the specifications, for example a copper (pre ZLincoln) is 3.11g +/- 0.13g 95% of the time (that last bit is frequently left off). So what does a single measurement of 2.95g tell you?? Nothing... It could be a 2.98g coin with some wear. It could also be 2.95g pristine but one of the 5%

In fact, this is the first time I've seen it. In previous discussions of tolerances, there's been an assumption that the tolerance specifies upper and lower limits on weight, and that the Mint should reject coins outside that range. If you expected 5% of coins to be outside weight tolerance, that would have big implications for authentication at TPGs, or for that matter in vending machines. (If 5% of coins can be outside tolerance, how far out can they be? Can a few cents weigh 6g? 60g?)

What it means is that if you were to weigh all the cents the Mint makes and plot them on a graph (x axis being increasing weight and y axis the number of coins), the result will be a bell curve and 95% of the coins will be between 2.98 and 3.24 grams. So 2.5% heavy and 2.5% light, and by the time you get to either of those tolerance edges the number of coins is decreasing RAPIDLY. In theory yes any weight would be possible (but there are realistic limits. A 6 gram coin would be twice as thick and a normal coin, a 60 gram coin would be 20 times as thick. There are limits as to what will pass through the feeding devices.), but by point of a second or third tolerance deviation the number of coins is approaching zero.

I would've expected the cutoff to be sharper than 95%. Is this codified anywhere, or just generally understood? It seems like I've weighed a lot more than a hundred unworn coins, and found a lot less than 5 that were outside tolerance. I'm not sure that I've found any outside tolerance, in fact, except for ones that subsequently turned out to be fake.

Tolerance for clad quarters is +/- 0.227g. Any weight between 5.443g and 5.897g is within tolerance. You have a normal quarter.