Firstly, I don't have any experience with Amazons, so if I'm talking rubbish, someone please correct me. I believe that some species do need a little more fat in their regular diet than others. I remember Michael mentioning this before, but I cannot remember what species he was referring to. I appreciate that attempting to trim weight requires a more specialised diet, away from the norm.
Is it necessary to have the pellet with dried fruit & veg in it? AS30 will have some of that, plus you're also providing fresh F&V, which Echo is taking? Roudybush also produce a low fat pellet. Again, I do not know if that is suitable for Amazons, alongside fresh F&V, but potentially worth considering once Echo's weight is where it needs to be.
It seems that a lot of vets encourage us to feed pellet. I discussed it with ours and it seems that they do it because a lot of keepers feed poor diets to their birds. Good pellet has the essential vits & mins that are missing if seed/parrot mix is the only thing provided. Most people on this forum are far better informed than those that have been (poorly) advised by shops or previous owners. A lot of the members here have also put far more effort into diet research and provision for their birds, and are able to offer expert, species specific advice. Our vet is satisfied that we are providing a well balanced diet and he has backed off on the pellet recommendation.
Let's face it, pellet alone would be seriously boring! Okay, it may be possible to provide a more accurate amount using only pellet. Assume X percent discarded/ejected/ignored and you may get a more reliable figure for what is actually being consumed.
As for weight monitoring, I try to do it before the birds have had anything to eat as it produces more consistent results. I use a kitchen scale than can be zeroed (TARE) when anything is placed on it. I use a homemade T-stand, zero the reading then pop the bird on the stand. Jardine Jessie is very accommodating, but Eclectus Frankie is a bit of a fidget (plus he is more interested in trying to bite me), so a stable reading can be a little harder to get
Budgies? No chance of weighing them, but they are all eating well and remain constantly hyperactive, so they all seem to be fighting fit!
I weigh them less often now as they both seem to be in roughly the right place for their species. I basically do it to check for significant changes which would need investigating.