Hi. Congratulations on your new addition.
It doesn't necessarily mean she is overweight, it depends on the size and build of your chihuahua. They vary in size hugely. The standard is between 4 and 6lbs full grown but on here there are Chis as small as 2lbs and some as big as 10lbs. It just depends on your individual chi. You should be able to feel her ribs but not see them, if this is the case then she's the perfect weight.
The amount or food she should be eating really depends on the food you are feeding. As she is a young puppy you don't want to worry too much about how much she is eating. Make sure that you're giving her 3-4 meals a day though and chihuahua puppies need food little and often to keep their blood sugar stable.
As for crying, I would leave her for short amounts of time and increase that amount bit by bit so she gets used to the fact that you're going to have to leave but that you're always gong to come back. When I left Mylo I put him in his crate and gave him his kong filled with treats so that he associated me leaving and his crate with good things. I'd also often hide treats around his crate. The most important thing is to wear them out either by playing its them or taking them for a walk, an exercised puppy is a good puppy. Then she'll most likely just sleep. If she cries when you leave ignore her as paying attention to her will reinforce the behaviour. Do not return until she is quiet.
Hope that helps