My 7 week baby is very gassy and seems full of air. What could be wrong?

Digestion. If you are breast feeding, look at what you have been eating. Dairy is #1 in making babies very gassy. If you are formula feeding, the baby may not like a milk based formula. Many babies are also gassy because they are not colonized with bacteria in their guts when being born . Many respond well to probiotics (for babies) ...1/4 tsp 2x a day..It is helpful to discuss with your pediatrician.
Varies. Gassy babies either make gas or pass on what they swallow while eating or crying.Germ action in the gut makes gas,and the fuel for this is material baby does not digest.Breast milk or formula may contain elements baby cannot digest and these increase gas. If your baby fusses a lot, it may generate plenty of gas, or baby may have problems with your diet (breast feeding) or the formula.