If you use kitchen scales you can set them to zero including the weight of whatever you are going to put the bird in or on. Our vet uses a plastic bowl or you could use a cardboard box if she is likely to not stay put (they love playing in boxes by the way). We use a perch I made that fits on the scales. At first we had to bribe Casper to go on with a bit of nut but he just steps up now as it is such a routine.
How to weigh a parrot by Jean-Pierre Declemy, on Flickr
There is an album of Casper pics on my flickr gallery.