Are values in Asset fields held globally for a particular Asset?
The fields attached to an asset source will be connected to the asset, and will follow the asset no matter where it's used. So yes, this is the intended behavior.

If you need to specify on an entry basis what size an image should have, you need to add a field for selecting size on the entry type. Say you have a field "Main image" in your entry type, you'd add a "Main image size" field to the same entry type. 

If you're making a gallery or something, instead of having one assets field where you select all images, you could create a matrix field that has one column for (one) asset and one column for size instead, and add each image as it's own row.