Re: minimum weight
It's probably something to do with design tradeoffs.
The problem is going to be that it's a zero, zero ejection seat. Meaning that should the F35 catchfire on the runway then the pilot can eject from zero altitude whilst stationary. This requires a fairly powerful explosive exit, followed by a very fast parachute deployment.
At a guess, the reason the timer is set to it's current setting is that if it's set to longer then if you do a zero zero eject then the seat could well hit the ground before deploying the chute, a not ideal situation.
If you then eject at speed, kicking out the parachute pretty much immediately is going to cause the ejection seat to go from the aircraft speed to a slow decent very quickly. So quickly that the helmet is going to cause the pilots head to get something like whiplash, which presumably has never been a problem previously because the helmets were just there to protect the pilots head, instead of having a ton of electronics attached.
They probably used a very, very simple fault impervious and time proven system like a burning fuse lit by the initial ejection charge because I suspect the Martin Baker engineers are probably more paranoid about system failure than most of EL Reg's readers. I guess somebody is having to design in a more untested and less fault tolerent workaround at the moment that checks how fast the seat is moving and how far it is from the ground etc.
The weight issue probably doesn't have much to do with weight in the seat per se, but how the pilot is built, ie people with strong neck muscles might get strained muscles, but slightly built pilots get broken necks. As telling people to measure people's neck with a tape measure is probably not an acceptable workaround, and given military fitness standards mean that body fat is not likely to be significant on pilots somebody probably figured that it wouldn't be an issue for >99% of people over $weight (+$FudgeFactor) as they probably have substantial enough neck muscles for this not to be an issue. Probably. Just guessing.