Thanks for you feedback... much appreciated!
I considered a range of options to secure the revolver caddy in place so it would spin well. There is no issue with it falling over... but unless the base is held in position it can spin along with the revolving caddy part. The simplest, easiest and most effective solution is to use Blu-Tack as noted in the instructions. Double-sided tape can also work okay. Adding a lot of weight into the base could help as you suggest but it still means it is not stuck in place which is what you want to ensure the caddy spins and the base doesn't. Making a thicker / deeper base will also compromise the look and, if you need to buy the weighting material, it will cost less to use Blu-Tack or double-sided tape.