Since you need to put each chicken into the room, and I guess at this stage
there would be some kind of inspection you can put a metal collar on each.
alternatively you could put it on their wings but it would not be as humane
to the chicken.

Since each chicken is territorial it would be safe to assume that each
chicken
would be no closed than 100mm from the other.

Several cables are lowered from the roof, on the need of each cable you have
an electromagnet, the Electro magnet is powerful enough to attach itself to
one of the collars. a feedback circuit will inform the system that it has
attached
to a collar and raise the cable up.

Since the chicken will not stay still for an accurate measurement you could
retract
the cable through a plastic funnel this would stop the chicken from
spreading it
wings and flapping about.

Attached to the cable is a strain gauge, simple calculation and you will be
able to
determine the weight of the chicken, you could also use the funnel to
estimate the
actual size of the chicken.

Alternatively you could use the funnel with a vacuum system instead of a
magnet
system, but if you use this system I'm not to sure how much vacuum would be
required
and if you are running the risk of sucking the guts out its beak/bum.

(I'm still all for the catapult idea)!

Regards
Andrew