Adhering something to a porous surface
Heavy things are easier, actually. Standard approach for a "non-penetrating" roof mount is to simply let gravity hold it, with suitable "load-spreaders" to keep the weighted feet from damaging the roof surface, and sometimes EDPM rubber to add friction. Easier on "flat" (low-slope) roofs, or on the peak of pitched roofs.

If you thought that adhesive was a good idea in that case (most don't, is roof damage can result when the thing needs to be removed, or when forces beyond what you planned for remove it anyway) hot roofing tar would be ideal - it's most of what "asphalt" is, so it's compatible, and it will act a whole lot like hot glue. Of course, you are then depending to whatever extent you have uplift forces on how well the layer of roofing you glued to is glued or otherwise fastened to the layers below it - which is another reason this approach is not normal.