To change the order of objects on the same tile, or to pick a specific object to delete from a stack, open the Mapmaker. (You must be an Admin or Builder to open the Mapmaker.)
With the Select tool active, click on the stack of objects/tile that you want to manage. In the right pane of the Mapmaker, the List of objects tab displays. Hover next to the name of the object and select the three dots to the right of the name. From this context menu, you can change the order of the object, delete it, or make a duplicate of it.
Note: You can also rearrange the object stack by selecting the two-line reorder icon next to the object name and dragging the object to its desired order.