They can certainly over eat and gain to much weight, but overeating to the point of sickness? I highly doubt it. If they get sick from eating a lot it is more likely WHAT they eat then how much.
Is yours getting sick, do you think he's eating too much?
Birds can most definately overeat, but not generally to the point where they will get sick. Just make sure your bird is getting a balanced diet. Your bird can become obese or overwieght, so making sure your bird is getting a proper diet is crucial.
I second what AD and DustyDusky say.
Perhaps the bird is eating too much of one particular thing.
Very important a bird gets a balanced diet.
Keep us posted
Great day
No he's not getting sick and right now we're being very careful about what we feed him. It was really just an fyi question. I know there are alot of animals that will overeat enough to make themselves sick so I was wondering. I have horses. They will overeat enough to kill them if they have access to the wrong foods