I would say that body fat doesn't strongly contribute to frequency of urination unless you are gaining or losing weight. Passively stored fat isn't doing anything at all, metabolically. On the other hand, difficulties in voiding bladder content WILL affect frequency of urination. Basically a physiological manifestation of "If you can't do it right the first time, you'll have to do it again until you get it right."
Your "metabolic rate" is a catch-all term that relates to your body's ability to process what you eat and drink. If you have eaten, your body will break down the protein and carb content, which involves "denaturing" (removing water from) the food. It is said that we are over 70% water. But because we ALL came from the same "tree of life," everything we eat is the same way - mostly water. Metabolism includes the act of chemical breakdown in our digestive system, where the water comes out as the proteins unfold, releasing what is called "water of hydration." I know it sounds like a tautology, but isn't because it is distinguishing between water that is strongly bound (water of constitution) from that which is less strongly bound (water of hydration). The primary sources of the water going through your kidneys are (a) whatever water is in what you drink and (b) water of hydration from what you eat.
To the extent that you have excess body fat, it is possible that the fat interferes with your other organs since fat cannot be so quickly stored in the body. It is, after all, less soluble in water. That management of fat is handled by the liver and gall bladder. As those organs lose some of their function with age, we find it easier to put on a few pounds because we can no longer process fatty foods so quickly. So to this fine point, Jon, it is true that extra weight might affect that frequency of voiding. But the simple direct link isn't there. It might be possible to lose the weight and still have issues with frequency of urination. The more direct link is the efficiency of how we process our food.