Her other 2 died from unknown causes.Are you sure about the age? Sellers sometimes misinform. If you're absolutely positive about his age being six weeks, he does have a serious problem.
At six weeks they're supposed to look like this - my goose at five weeks, six days:
How do the other two look? Is he very different from them? If none of them are looking age-appropriate, they're probably not getting enough to eat.
Have you tried weighing him/them? At six weeks they should weigh about 8 lb. Mine weighed 8 lb. 6 oz. when she was six weeks old.