How well would the average human get around if they packed on 300, 400 pounds to their frame without any increase to strength?
Very poorly. The average real life human of that size also doesn't have the game reality equivalent of an "elite pro" athletic capability, though. Those two things do not logically compute at all, but they do in the mechanics of this game world.
And STR 1 isn't average, it's BELOW average.
That is what I said above. No contest, I agree.
So, with the strength of a 98 pound weakling trying to animate a body the size of a troll... is it REALLY vindictive GMing to say you're having trouble going up stairs?
It depends on how it is implemented. If we are adding mechanical penalties where none exist in the game world, that is vindictive. GM doesn't like the way player build their PC, so GM is punishing them with game mechanics for it. It is the textbook definition of adversarial GMing.
If we are making notes about role-play elements, like he slowly struggles his way out of the chair, slowly struggles his way up the steps, ect. when it doesn't mechanically matter, then all of that is both totally cool and encouraged.
Besides... carrying capacity is an objective rule. It may not be commonly enforced, but if you go out on thin ice you're asking for it to be. Granted, carrying capacity is implicitly only talking about stuff beyond your potentially corpulent frame, but still how much do you think a set of troll sized clothes weighs? How about ARMORED clothing in troll size? STR 1 is pretty much encumbered all the time anyway... if you actually enforce that rule.
And this is part of the problem with incomplete rule sets, like assigning weight to items. With a lack of proper item weight / carrying capacity, I personally would resent receiving a heavy penalty over what is essentially non-existent mechanics. On the other hand, I personally would also be totally fine receiving reasonably light mechanical inconvenience. If we wanted to say Fat Larry is a bit slower due to his armor (in addition to the speed reduction the armor already imposes), I would be cool with that. If he walked around for hours in the armor and we wanted to have him make Body + Willpower rolls to resist Fatigue levels, I'd also be cool with that personally.
Now obviously if he actually tries to lift heavy things, despite having that titanic body + willpower dice pool for it, I would personally just say things like "Fat Larry makes a valiant attempt to help the strong guy lift the heavy thing, but after several seconds of huffing and wheezing, he resorts to just lethargically leaning his own mass against the side of the heavy thing, leaving strong guy to do all the work.".
*EDIT: Ok, I CAN see a rationale for 8 Athletics and 1 STR: You're a former olympian who suffered a debilitating disease/injury, and you only went down to 1 STR after developing phenomenal athletics.
Edit for your edit:
Yeah, that is one example of how one could apply some form of logic to make it more reasonable.
Personally, this is where I fall, both as a player and GM. My #1 object when GMing is to just make sure my players have fun. My #2 objective is running the rules as written, so that everyone learns those rules appropriately. So long as a character is legal, I will let absolutely anything fly without additional hardship, even if I personally don't like the build, because I want my player to have a good time playing what they designed.
As a player, character building is half of my whole fun in gaming. I also want to be permitted to play my legal character without added hassle that doesn't exist in the mechanics, unless I agree to them for any valid reason I may choose. Sometimes I design ridiculous but mechanically accurate characters like Fat Larry, sometimes I design ones that are far less controversial. The only consistent in my builds is that they will be min-maxed to some degree, because that is what I enjoy.
To each their own, though. Everyone should play in the way they have fun. If one feels the need to judge anyone else for their play style, there are conveniently lots of people who will share your personal views to play with.