Attaching a heavy plastic object - of which I can't access the inside - to the side of an office table
Why not create a shelf-like support using two or three angle brackets to support the weight of the docking station? 

The vertical leg of the bracket could be screwed into the side of the desk, and the horizontal leg (in the down position) would carry the bulk of the weight. Then the hook and loop style hangers would only be holding it tight to the desk (horizontal pressure) not carrying the weight (vertical pressure).

If the horizontal leg is too long, it could be cut off with a hack saw.

A more elegant version would be to build a wooden shelf to support the weight, but that would be a bit more complex to ensure its strength to carry the load.