Why Trimethylamine is weaker base than dimethylamine ?

In gaseous phase, Trimethylamine is more basic while in aqueous phase, Dimethyl Amine is more basic.

This is because in aqueous phase, the substituted ammonium cations ( conjugate acid) get stabilised by not only the inductive effect of alkyl group but also by solvation by water molecules.

The order of basicity is as follows :-

(CH3)2NH>CH3NH2>(CH3)3N>NH3aqueousphase(CH3)2NH>CH3NH2>(CH3)3N>NH3aqueousphase

Dimethylamine is more basic because when all alkyl groups are methyl then basic character follows this order

2 degree > 1 degree > 3 degree > benzylamine > ammonia > aniline