In a word... no But, if it's an old, well used machine, yes it could. If the ground cable is badly worn and/or you have a loose connection to the clamp, that can cause a reduction in power... so replacing it will improve things. Won't make any difference on a new machine though.
weldequip
Are you running it off a long extension lead? That won't help any. 70amps is very limited as to what it can do...3/32" absoloute max I would say. Maybe you are trying to get too much out of it.
weldequip
Edit: I was thinking MIG You'll get more than 3/32" from MMA...1/8"+
I don't know what you mean by a "jumper int he fuse box"
You can install a new breaker and a dedicated run to the garage. 12/2 should work. You will have to check codes on what you can run. Run inside wall can probably be Romex, anything else would have to be conduit or armored cable.
I bought a 20A extension cable for my MIG. Made a big difference over the regular 15A ones.
I use my auto on 10 or 11 depending on what I'm doing. Best thing is to try it on a darker setting then lighten it if you can't see properly, and keep going until you find what suits you best.