Get two washing up bowls, one larger than the other. Put the smaller bowl
one in the larger bowl, and fill it with water. Put the first cat in the
smaller bowl, it'll most likely get out of it's own accord. You can then
pour the water displaced into the larger bowl into a measuring cylinder,
and using a rough density of water as 1ml = 1 gramme, work out the weight
of the cat. Of course, the cat is likely to retain water in it's fur, so
it may be a good idea to cover it in vaseline first to minimise errors.

Then repeat the process for the second cat.
Even simpler, put the water in the outer bowl and float the inner in it. Put
cat in inner bowl. Provided inner bowl does not "bottom" the weight of water
displaced is exactly equal to the weight of the cat. No vaseline, no density
correction. Archimedes rules OK!