In this word. we have a root ie.. veter--that have lasted a long time and seem likely to continue. This itself gives an idea of the meaning.
World war II veterans. veter is a root which means for a long time
in + veter (water) + ate -> even in water (flood) a deeply rooted tree will stand still...
Inveterate = in wet(vet) ra tea tagudam...its a habitual, deeply rooted, firmly established thing to have when the climate is wet..
He had the habit of collecting information about different animals and he chose to study vet (veterinary) as his professional course.
Inveterate = In + better + ate; He ated in good manner so he will lasting long.
These veteran smokers are inveterate smokers