My opinion is that if the weight of the hanging object causes the branch to bend down much, then move it a little closer to the trunk of the tree where the branch is stronger. If it’s a very new, young tree you might want to wait before hanging anything in it. I can’t imagine that a tile would be heavy enough to do any damage unless it’s a huge tile and a spindly tree.

If you are concerned about the cord damaging branches, you can put a piece of gardening hose, aquarium tubing, or anything like that on the cord where it touches the branch. Or wrap the branch with something. Most things we hang from trees like bird feeder‘s and bird houses are pretty light and would be fine.

i used bungee cords ....

one hook in left hand.. twice around the branch and match second to first .. then hang from the two hooks ..

soft ... pliable .. will expand with tree .. will eventually rot off if necessary ...

for one very large wind chime on a large oak branch.. i used the flat black rubber version ...

ken

Excellent ideas, thank you to ken and socks!!