Do you own a gram scale or do you only have your birds weighed at the vet?
I think a gram scale is one important thing to own; since birds rarely show signs of illness before they get severely ill, weighing them can give you some insight before it's too late. A significant drop in weigh could indicate that something is wrong and a preventive visit to the vet might be in order.
It is also important to establish what is your bird's "normal" weight. Although there are charts out there with average bird weight per species, sometimes there is a variance depending on subspecies. This variance can be significant depending on the species so knowing where your bird is situated can help you figure out if he looses or has gained weight.
A bird's weight will vary from a couple of grams within a day so it's important to weigh them around the same time to have a true idea of the weight gain/loss.
Finally, scales aren't that expensive. I know people who have got them off e-bay for cheap. I got mine (I have two) in two different places; I got one in a specialty kitchen store for about $20 and I got one on sale at Canadian Tire for $10. You don't need them to be extra precise; anything less than a gram in difference isn't that significant for them. Just make sure you get one that will go up to your birds weight (I'm thinking big macaws and big cockatoos might need something different than your average kitchen gram scale
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