Why are potassium organic salts ever preferable to the sodium equivalents? $\ce{KOH}$, $\ce{KCN}$, $\ce{KNO3}$, $\ce{K2CO3}$, and plenty of other potassium salts are frequently used in industry.  But, as far as I can see, the sodium equivalents are also widely used, often interchangeably.  Since Na weighs only 60% of K it seems like the sodium salts should always be preferred because they carry more of whatever base is attached per unit weight (i.e., the sodium salts have "more of what you want"). $\ce{Na}$ is also slightly more abundant (on earth) than K.

So what other factors favor the industrial use of K-salts?  E.g., are K-salts just more abundant in natural sources?  Are they more reactive because the ionization energies of K are lower than those of Na?  Are the behaviors of these simpler salts actually different between the K- and Na- variants, and if so, is there some other elemental characteristic that suggests this?

Going the other way, it seems like if K is preferable to Na, Rb should be even more so (because it appears that in every elemental characteristic in which K exceeds Na, Rb exceeds K).  Would it be if it weren't so relatively scarce?
The differences in the properties of the alkali cations are subtle, and the rationale for choosing one over the other will depend heavily on the application. I suspect you're right, that to some extent natural abundance of, e.g., potassium salts relative to sodium ones in certain mineral contexts explains the industrial preference for one or the other -- but, really, variations in abundance are just further examples of these subtle differences in the properties of the cations!

One specific example that I recently came across is the Hofmeister series (see also the Wikipedia article), where the choice of cation makes a demonstrable difference in the solubility properties of proteins.  Speaking also from personal experience, the choice of, e.g., $\ce{Na2SO4}$ versus $\ce{K2SO4}$ versus $\ce{(NH4)2SO4}$ as a component of the supporting electrolyte in electrodeposition of copper from acidic $\ce{CuSO4}$ matters significantly to the properties of the deposit obtained.