Something that you need to keep in mind, especially with an Amazon because they are extremely prone to this issue when they become overweight at all, is that the likelihood of your bird starting to develop "Lipoma's" all over it's body...If you look in the Amazon forum right now, the 1st or 2nd post is regarding an Amazon with a large, soft growth on it's chest area, and it's likely it's first Lipoma.
Lipoma's are tumors that initially consist of only lipid (fat) tissue when they first develop, and the cause of them is simply because they are overweight, and extra fat-stores and cells start to form into encapsulated tumors, and these fatty tumors typically develop all over their bodies, and are typically plentiful; birds who are overweight/obese often develop dozens of Lipoma's all over their bodies...And for whatever reason, Amazon's in-particular are extremely prone to both obesity and to developing multiple Lipoma's all over their bodies.
***The danger of your bird developing Lipoma's (in addition to him developing Fatty Liver Disease, which he most likely already is suffering from), is that even though they are benign and do not usually post a cancerous threat, they do however pose other very serious and often fatal complications. If a Lipoma develops, typically Avian Vets don't like to remove them, because of the major risk that anesthesia poses to all birds. So typically the treatment for Lipoma's is to simply get the bird to lose weight and burn fat-cells, thus shrinking the Lipoma(s). However, they never go away completely, and they are encapsulated, so they will always be there once they form. So if the bird never loses weight, or if they lose weight and then gain it back, the Lipoma's that the bird has will continue to grow, and depending on where on the bird's body the Lipoma's are, they can become large enough that they either form their own blood-supply, OR start to "steal" the existing blood-supply from a neighboring organ, OR they can of course grow into/attach to vital organs, or a combination of all of these.
If and when Lipoma's develop their own blood-supply or grow into a neighboring organ or it's blood-supply, then that's when they usually become totally "inoperable", and if they start to rob a vital organ's blood-supply, this can obviously kill the bird. Lipoma's can also cause permanent disabilities in birds if they grow into nerve supplies, grow into muscles, or more devastatingly they grow into their spinal column, into their cranial and/or facial nerves that supply their eyes, ears, sinuses, etc., or if they grow into an area of their body that makes it impossible for the bird to move/walk/fly normally, or at all, such as on their wings, on their legs, around their vent/cloaca area, etc.
****Bottom-line is that when most bird owners are told that their parrot's are "overweight" or "obese", they automatically think about issues such as Fatty Liver Disease, Heart Disease, Strokes, problems flying, etc. (or other pet owner's for that matter, as this issue effects all types of pets, from dogs and cats to very often occurring in rodents). But what they don't think about are the most common issues caused by their bird's being overweight, the most-common issue being the development for Fatty-Tumors or "Lipoma's", especially in ALL SPECIES of Amazons.
I don't know why Amazons are so plagued by Lipoma's (Amazons develop Lipoma's at least twice as often than all other species of parrots combined, that's how common they are in Amazons), maybe it's because Amazons are just more susceptible to becoming overweight/obese than any other parrot species in the first place, I don't know, but I have seen many, many obese Amazons at the Rescue compared to any other parrot species we see. Either way, if you Google search "Lipoma's in parrots" you'll see not only how common they are, but also how serious these simple, Fatty Tumors can become.
***Something else to keep in-mind is that it's not the amount of food you feed your bird, but rather the kinds of foods you are feeding him. Birds like to eat throughout the entire day, picking at their food sporadically in little sessions throughout the day, all day long, and that's fine, this isn't the issue. And believe it or not, even if your parrot was not weaned onto a daily staple diet of pellets but rather onto a daily staple diet of seed-mix, or if you're having issues getting your bird to transition from a daily staple diet of seed-mix to pellets, that doesn't mean that your bird is automatically going to be overweight or develop Fatty Liver Disease!
In recent years with the huge "push" by some Avian Vets and from the information found on the internet to switch all of our pet, captive birds from a daily staple diet of a seed-mix to one of pellets, it's very difficult to still get the point across that there is a huge difference between a healthy, low-fat, varied, fortified seed-mix and any of the MANY unhealthy, high-fat seed-mixes that are readily available everywhere, and that are very cheap. I am one of the long-time parrot owners and breeders who believes that it's important that my birds still eat seeds, legumes, grains, etc. every single day, as their bodies, specifically their GI Tracts from their crops downward, are designed to digest and process seeds, as are their beaks, and more importantly, their brains. Pellets do not exist in nature, they are totally man-made, and as such our birds do not ever innately look at a pellet for the first time, even as unweaned babies, and say "ooh, pellets!". I have always fed all of my parrots (not my Dove, obviously) a main, daily staple of a Natural-flavored Pellet (no Fruit-flavored Pellets, as they are full of sugars, which simply end-up as stored, unburned fat in captive birds), IN ADDITION TO a small, daily amount of a healthy, low-fat, fortified seed-mix, and then fresh veggies every single day.
So the point is that it doesn't have to be all-or-nothing, and it doesn't have to be one-extreme or the other! If your bird has always been fed a daily staple diet of seed-mixes and has not and will not eat pellets, but you are desperate to improve their overall health and nutrition, reduce their weight if they are overweight/obese, reverse a diagnosis of Fatty Liver Disease, shrink-down Lipoma's that your bird has on it's body, etc., the first step should NOT EVER BE going out and buying a bag of pellets and suddenly just trying to switch them over completely to pellets and no seed-mix at all,
as usually this doesn't go well at all. The very first step in this process should be going out to a pet store, not a grocery store or department store like Walmart or Target, and choosing a new seed-mix that you can start feeding your bird right away and that they will willingly start eating right away (usually) that is healthy, low in fat,
low in sugars, that contains NO SUNFLOWER SEEDS OF ANY KIND, No Peanuts or other Nuts of any kind, No Corn of any kind, but rather contains an extremely varied mix of many different types of healthy seeds, legumes, grains, dried veggies and fruits, and in some cases, such as with Tropimix seed-mix, they even contain a healthy pellet in the seed-mix. Simply changing your bird's daily seed-mix from a high-fat, high-sugar, high starch, junky one to a high-quality, healthy, low-fat, low-sugar one will make all the difference in the world to your bird's overall health and nutrition. THEN, once you make this change which is drastic and huge to your bird's health yet not a big deal psychologically to your bird, THEN you can start to gradually transition your bird from having their main daily staple diet being a seed-mix to being a Natural-flavored Pellet. If you do it this way, you're immediately improving your bird's overall health, weight, and nutrition without feeling like you have to immediately force a transition onto pellets, which usually takes times and can be tremendously stressful for your bird.