organic chemistry - Why are double bonds at more substituted carbon more stable?

That $\ce{C=C}$ bonds are more stable at more substituted carbon atoms is a common argument used throughout Clayden et al., but is never actually explained (at least not in the first 21 chapters). They do explain however, why the HOMO is increased in energy for more substituted double bonds, through the argument of electron donation by means of hyperconjugation of neighboring groups, increasing the electrophilicity of the $\ce{C=C}$ bond.

I find this somewhat counterintuitive. Usually when something is more reactive, it is less stable (I understand that of course by kinetic pathways this does not always hold, e.g. with $\ce{I-}$ as nucleophile).

How can both observations be incorporated in a consistent explanation in this case?