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..
invert + rate >>> yane jab koi shopkeeper ya koi bhaji wala rate bolata hai, tab womens ko AADAT(habitual) hoti hai bhaav karne ki
Inveterate = In + better + ate; He ated in good manner so he will lasting long.
These veteran smokers are inveterate smokers