There are a couple of options for weighing untamed birds. Simplest method is take a container that will fit on the scale, like a cardboard box or even a travel cage, if you have a big scale or a small travel cage. Put it on the scale to zero it out, then put the bird into the container to weigh it. They can't fly off in the middle of the operation and usually settle down once they are contained.
Another hands-free method, if they are slightly tame but will not tolerate being grabbed, would be to train them to land on a T stand perch or similar and then put the perch on the scale to weigh them.
Sometimes just putting the stand on the scale is enough and they will land there on their own out of curiosity.
I am thinking of something like this:
Amazon.com : ZOHOKO Parrot Training T Stand Perch, Small Tabletop Bird Stands Perches for Conures Parakeets Lovebirds Cockatiels : Pet Supplies
www.amazon.com
If you forget to zero out the scale with the perch on it, just write down the combined weight and then weigh the empty perch and subtract it to get the bird's weight.
Another option involves time and sneakiness, but might be the best option for budgies that resist training and don't do hands. Set-up the t-perch somewhere the budgies like to land and teach them it is a great place to find free millet. Next, position the scale under the perch and continue to offer millet and treats at this awesome location. Lastly, add a millet spary or similar treat, then zero out the scale and wait for one of your untamed budgies to land while pretending to be uninterested in the totally awesome millet perch. Read the number before they fly off. Mission accomplished.
Ideally, you want to make it easy and rewarding for the birds to land on the scale so it isn't a traumatic experience for you both. Not always easy, but definitely possible.
