May one adjust the height of a shtender on Shabbos?
Yes. This may be done even if it involves loosening and tightening screws, as it is not made to last even temporarily. However, some Poskim are stringent to forbid doing so being that at times one does leave the Shtender in the adjusted position temporarily for a few days.
 Piskeiy Teshuvos 9:38
 So rules Az Nidbaru 14:11 and Sheivet Halevy 6:32; Shulchan Shlomo 313:7
 Minchas Yitzchak 9:38