Is this a trick question, as you normally show a lot of knowledge of oil formulations and this is a basic question., but to the best of my knowledge which is not expert in this field, and from my understanding of the question, it is something else.
TBN is a measure of the very mild alkalis or buffers being added to neutralise the acids in blow by.
Viscosity is dependant on the molecular weight of the base stock and added viscosity improvers which are chemicals that get thicker rather than thinner when heated and so offset the thinning of the base oil when heated. This allows light base oil to be used without it thinning out to much at higher temperatures.
If one additive does both jobs, it is a fortunate coincidence.
Regards
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