My guess is the doctors couldn't find a vein on her arm because of the fat, so they chose the least fatty place they could find: the top of her hand. I've had an IV put there because the doctors couldn't find my vein because of dehydration, it's a pretty normal place to put an IV if other parts of the arm are unavailable for reasons such as dehydration, having damaged veins on your arm, or as we can see here being a fucking lardbeast.