Funny thing is, I'm not by a big guy, but I remember wondering about essentially the same thing, and I think around the same time in training too (about three years in).
Thing is there isn't a final answer to this question. As you already know, for an experienced nage your size shouldn't be a problem. If your size is a problem, then nage has work to do, and you shouldn't expect things to go in an ideal way. So yes sometimes nage might resort to atemi, and then your practice as uke might be to practice dodging atemi. Or you might decide that attacking any stronger is too risky and then nage just has to accept that he or she isn't getting a stronger attack for now.
There's always some kind of compromise involved in practice unless both of you are very experienced....no actually there's still some compromise even then, just maybe the edges get a bit sharper and the lines thinner.
Keep looking for the edges.