Birds don't show that they are ill often until it's too late.
And while in the past I haven't been as thorough as I am now about actually weighing the birds, I would do it a few times a month, around the same time of day, so that the values would be taken around the same time.
A few months ago I decided I wanted a more precise baseline - while I had a general idea of each birds weight, I wanted to have more values in a smaller amount of time so that what I knew as their weight would be more precise.
I now take their weight every second day, and always after diner once I let them out of their cages. This might vary by half an hour from night to night, but it generally means they would have had diner earlier or later so the amount of time between when they get food and come back out is about the same.
The main reason I wanted to more accurate baseline was Piper. The last few times that I left him in the care of someone else for a few days he always seemed to be lighter when I got him back. Didn't matter if it was two days or a full week, he would loose weight.
I am actually keeping a spreadsheet with all the data - have been since I started weighing my birds somewhat regularly from 2008 onwards, and I have, for this year, added a comment column so I can take notes of things that might explain a variance in weight - being birdsat, an injury, a delay in when the birds were weighed - anything.
While there are very expensive scales for sale specifically for birds/parrots, you don't need to purchase one that costs so much. In fact, I got mine for sale for $10 (regularly $30). I've had it for years and it works great. It's only precise to the gram but that is plenty.
Link to the one I own - The scale.