Trees growing around objects vs pushing them away. Where is the threshold?
Since you asked for the science I'll try to give a scientific but simple explanation.
Trees (and plants) become wider and taller over time. This growth is due to cell division and cell elongation from meristematic cells (analog to stem cells in animals).
The stem (upper part of a plant) becomes wider because is it constantly creating new vascular tissue from the cambium. The cambium creates xylem to the center of the tree and phloem to the outer parts. The bark that peels off is the phloem and other tissues irrelevant for the explanation. Here you can find a good illustration.
Since the tree adds new xylem all the time the, cambium gets further away from the center of the tree.
When the tree pushes against a wire, the wire cuts and kills the phloem cells and after that the cambium cells. But the plant has mechanism to regenerate the cambium ring and that's why the tree continues to grow there. In the photo the wire is already in the xylem section.
When the tree pushes against a wall there is a barrier in the whole section. Either the wall collapses (or, more commonly seen, the sidewalk rises) or growth in that sections stops.
I saw graphs of cells having up to 3MPa of turgur pressure but the actual pressure you should check is that of the bark which can be higher or lower. It changes between plants species, sections of plants and plants itself so the best is to simply check.
I wouldn't hang a weight from a tall tree. Trees get diseases and many times you only see that they are rotten from the inside when it is too late.