The inductive effect with the polarisation of the C-N bond obviously plays a role in stabilising the positive charge of the conjugate acid. But given the similar electronegativities for C and H, CH3 group should donate as much electron density to N as H does (roughly), if only the bonding atoms are considered. And if we're considering atoms other than the two bonding atoms in their contribution to stability, is it not a question then of hyperconjugation?
This question seems to deny hyperconjugation plays a role in stabilising ammonium derivatives. However, it takes a very narrow view of hyperconjugation and focuses only on electron density donation into bonding orbitals. But if more substituted double bonds are more stable because of the donation of alkyl groups into pi-star orbitals, antibonding orbitals must be viable recipients. And similarly in methylammonium, we have sigma-star orbitals on the positive nitrogen which the C-H bonds of the methyl should be able to donate into, destabilising the N-H bond in methylammonium but overall stabilising the system.
So, my question is does hyperconjugation from sigma C-H bonds into sigma-star orbitals of sp3 centres occur, and then from that - does hyperconjugation explain methylammonia's strength (or alkylammonias' strength, more generally) relative to ammonia?