I'm guessing you have to all take turns with early shifts? If that's not the case and you are able to ask for later shifts then you could do that.

The boxes thing. If you are being singled out and given bigger boxes you can't manage then that is clearly something that needs to change. If you have an injury or accident because of a heavy box you couldn't handle this could be serious- and not in their interest either.

Is there a responsible staff member who you can report this to safely?

My instincts would be to try to resolve before you leave but like others say maybe you should start looking elsewhere.

You mentioned your transitioning and I am unsure if that means you are being treated differently or unfairly in your workplace?