About Murphy and the AT-4. Not loaded it weighs just under 15 lbs. It is recoilless; so no kick but she would probably still feel it when she fired it. Just the vibration caused the firing an AT-4 could probably be very painful for someone with an injured shoulder, but it's a one shot weapon so she would only have to do it once. Unless Murphy was firing the AT-4C, she sure wouldn't want a wall or any other obstruction directly behind her. That vented gas is dangerous to anyone directly behind the weapon and a wall would force the vented gas right back at her, ouch!.
Fun fact: It's legal to own a rocket launcher in the U.S. Though the AT-4 round isn't actually a rocket, but I digress. However, the AT-4 tube is labelled as a hazardous material, or it contains hazardous materials. It's not something you'd want lying around the house.
I guessing with an adrenaline rush Murphy could probably manage to lift the thing once; plus, I believe only one of her shoulders was injured so she could probably manage it one way or another. Murphy's main problem is that she has no mobility. She can't shoot and scoot. So, being on top of Marcone's fortress is a reasonable place for her to be; being out in the street, not so much.
Her first problem would be getting to a fight. Murphy would probably have to be driven there unless Harry opened up a way that physically was only a few feet away even if it took her several miles away from her starting point. She'd still have to lug the AT-4 around. It makes far more sense for Murphy to driven somewhere, get dropped off and set up on the exact point on the sidewalk where she was dropped. Again, she has no options if Fomor aren't stopped dead in their tracks because she can't fall back at anything faster than a slow walk. At least she wouldn't have to lug the AT-4 around with her seeing as it's a one and done weapon.