As far as her weight, she does sound at 53lbs. to be on the small side. Does she finish all her food every day? If she does & seems to still be hungry she may need more. But, best thing is to ask your vet what s/he thinks of the pups's weight. She's still a growing girl, and sometimes they are a bit lanky. Depends, too, on how tall she is. Also, she probably won't be completely grown & filled out until she's about 3 years old. It is a good idea to NOT overfeed these large-breed, fast-growing dogs so as to avoid orthopaedic problems.
As for the standing up to get a look at things...I know Akitas like to do that, seeing as they're so curious about things. You can certainly make her stop it & get down when you see her doing it, but be consistent or she'll get a mixed message. The nibbling/biting on your hands may be nothing. It's hard to say since I haven't seen it. But, a lot of pups mouth, and depending on what kind of nibbling/biting it is, it MAY be that she's trying to groom you. If it's harsh or bothers you, a way to stop it is when she starts to do it, yank your hand away and squeal like she hurt you. Then, walk away from her. She'll get the message pretty quick not to do it.
It doesn't surprise me that she reacts differently to you & your wife; my Akitas react differently to different people, and it also seems to be sex-based. For instance, my male Akita loves women, but I think he tends to respect men more. My female Akita goes gagga over some men, though she's typically great with women, too. You need to make sure that both you & your wife work with your pup on obedience, since it's important that she obeys both of you. But, I expect that her response to each of you will always be somewhat different.
