Can one place a siddur on a tree or lean on the tree without moving it?
A. Mishna Berura (336: 3) explains that the ruling of Shulchan Aruch that it is prohibited to use a tree on Shabbos, includes not placing any objects on it. On the prior seif (2) he mentions that one should also not lean or support himself on it.
On (336: 13) Rema writes that one can touch a tree but not move it. Biur Halocho (ibid) debates whether when not moving it one can completely lean on it.
Horav Shlomo Miller’s Shlit’a opinion is one can lean on the tree slightly, when not moving it.
Rabbi A, Bartfeld as advised by Horav Shlomo and Horav Aharon Miller Shlit’a