The sum of ASECWT in the 2020 ASEC is about 240 million. I am assuming this number is lower than the 330ish million U.S. population found elsewhere as it reflects the adult non-institutional population living in the USA rather than all persons living in the USA?
When I sum the ASECWT values for the 2020 ASEC I am getting ~325 million; this roughly corresponds to the civilian non-institutionalized population (which is the target population of the CPS–see page 2 of the 2020 ASEC codebook). I wonder if you are restricting your sample based on age or some other characteristic and if this is the source of the lower sum you are seeing. Using 2019 1-year ACS data, I estimate ~239 million persons are aged 15 and older and have no military service (though this count excludes veterans and persons who are Training for reserves or National Guard).