Depending on the size of your rabbit you're looking for a collar that releases if you tug with the pressure of one/two fingers. Try to match the power that your rabbit will exhert in the initial moments they're caught up to minimise injury as much as possible. Remember, strangulation is just one possiblity and you really want them to be able to escape way before that happens.
This test should be a good indicator that if they get snagged that the collar will break free. I wouldn't personally suggest putting a collar on your rabbit as it just adds to risk.
If it's for walking I'd put him/her into a harness so even if they do panic you're not in danger of pulling against them and breaking their neck/strangling them. I've had some unfortunate experience with dogs doing very similar things.
If it's for an identification tag then a microchip is a fantastic alternative!
As for the question of how much weight is needed... Well that's difficult as most release collars release to pressure or force applied and not the weight itself.
For example, a rope can hold out for a longer length of time if it's just weight leaning against it but, if you were to apply force and pull the rope quickly it would be more likely to snap .
My answer to the title question:
I would say that 1-2lbf should break before the 'average' rabbit is strangled.
Possible solutions to rabbit collars:
Paper or very thin card collar. To make this collar simply measure around your rabbit's neck and then cut a strip of paper. Write your details on this strip before applying a small amount of glue to the ends and putting it around your rabbit's neck.
A light piece of string with a quick release knot: It's very important that you tie the quick release knot the right way or else it will get tighter instead of releasing. This is a similar technique that we use with Horses.
A make your own Velcro collar: Find some material you like and sew or glue small velcro straps to the ends to ensure it doesn't take much pressure to release. This comes with the added advantage that if your rabbit gets lost and looses the collar you have some idea of where s/he went.