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Typical incubation time in African Greys is 28-30 days with some variation for hatching of the chicks based on when their egg was laid in relation to the rest of the clutch. If she is only 21 day in then there is at least another week or more to go before we can say that the eggs are at maturity and should be hatching. The aggressive behavior you describe is referred to "broodiness" and a female exhibiting this behavior is said to be "broody". It is not uncommon for a female to focus on incubating and protecting her eggs or chicks but since she has lost weight, I recommend a veterinary exam to rule out other causes of weight loss. Additionally, a proper diet is important during this time. She should be eating a high quality pelleted diet with fresh fruits and veggies and may need a calcium supplement.
But if i can have a little more information about your bird and the situation will help me to advise you appropriately. Please forgive me if these questions seem simple, I do not know your situation and I am just trying to make sure that we re not missing s big part of the picture. Have you candled the eggs to make sure they are fertile? Was this a planned clutch? Has she or the male had a successful clutch before? Is she on an adequate diet for reproduction? Are the eggs in a proper nesting place?
If you need to remove the eggs to candle them to look for a chick, you can take a piece of PVC pipe that is wide enough to put your arm through and cut one side at a 45 degree angle. By slipping this over the egg, you can grab it safely without risking injury to your self or your bird. You can then use this same technique to replace the egg once you are done doing what you need to do. If the eggs are infertile, they should be removed and her behavior should return to normal within a few days. If not, then she should be examined by an avian veterinarian to make sure that there are no underlying metabolic issues.
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