I suspect you are looking at this from the wrong angle...
Load Factor, by definition equals Lift/Weight.
Therefore if you purely have an increase in aircraft weight, whilst lift remains at a constant amount, load factor will decrease.
If you were to increase lift as you increased weight, so that the two remain equal, then load factor remains constant.
To relate it to your C172 vs B777 example, the b777's wing must produce more lift to counter its higher weight, but if both aircraft are in straight & level flight then both have an equal load factor, ie 1.
Hope this helps!