Casper gets weighed once a week (Fridays unless we forget) and his weight is noted in a little blue book with any other topical information.
Since we got him, when his weight was a portly 450 grams, he has yoyo dieted between 400 and 450 but seems to have stabilised at about 420 for the last few months.
Here is a pic of the perch I made him to go on the postal scales
How to weigh a parrot by DSdriver, on Flickr
and here it is with Casper demonstrating how to use it
How to weigh a parrot by DSdriver, on Flickr