I don't know that I can answer why trimethylamine should be less basic. I don't think it is the only instance in which the acidities do not follow an expected pattern. I have pointed out the (di and tri)fluoroacetic acid(s) do not follow the expected trend. Generally a fluoro substituent is less electron withdrawing than the other halogens, compare benzoic acids, phenols, anilines, haloforms, haloethanols, rate of leaving group, haloacid acidity, etc. I certainly cannot explain why fluoroacetic acid should be more acidic than chloroacetic acid. It isn't that this result cannot be explained, but I don't know the reason.
If you compare ammonia (9.21), ethylamine (10.64), diethylamine (10.98), and triethylamine (10.65), there is an increase in basicity from ammonia to ethylamine. There is a smaller increase in basicity in diethylamine and small decrease in basicity in triethylamine. A similar but smaller decrease in basicity occurs. If you compare other amines, it appears that a methyl group does not give the same result as an ethyl or other alkyl groups. (See http://research.chem.psu.edu/brpgroup/pKa_compilation.pdf
.) Could the measurement of the pKa data be more complicated than examining a structure would suggest? Let's look at hydronium ions. Perhaps it also is not as simple as we might have expected, see http://www.lsbu.ac.uk/water/ionish.html
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