Ok, so I've been playing FO4 since the first day it was out, and have multiple higher level characters. But I never once invested in the Strong Back perk, figured it was a waste of points. I got the Lone Wanderer perk to add carry weight, put deep pockets on all my armor, and stray STR points from gear. It all helped, but I'd still often and inevitably reach that wretched moment where you're deep into an instanced dungeon or building somewhere, and you can't carry any more. So you either have to trek back out and dump/sell a bunch of stuff, or start leaving stuff behind. So I finally broke down and put four points into Strong Back just to see if it was worth it.
Oh my, is it ever! Now, when I reach my weight limit, I just keep fighting on and picking up all the goodies I want to. My 470-lb weight limit char brought home over 800 lbs. of goods once, yesterday. I had misunderstood the bonus from the third point in the perk, which seems to say you can use only use AP points to *run*, while overloaded. Well, it doesn't matter whether you are running or sneaking, it all just uses AP points to let you keep moving at your normal pace, without having to hold down any keys or do anything special. Of course, it helps to have plenty of AGIL and END, to extend your AP bar for this. Sure you have to stop every so often to let your AP bar refill, but with Action Boy/Girl perk, it's pretty quick.
So when yer done in there, you just jog on out like normal, and fast travel home with your bazillion-pound load all on board, no problems. You settlement scrounger packrat types really need this one.
Likin' it!