
I'm guessing his colleagues think calling him 'fat" is a major insult, if anything it says more about them and shows their immaturity. The character you it was directed to wasn't even overweight, let alone obese (not that that is even relevant). In another manga's comment section, someone referred to a disliked character as being a "fat hyung' despite him also not being overweight, I guess for some people it is just used as an insult, a bit like how people think age, and calling someone "old" is putting a person down.
This comic I guess is set in South Korea, which also has a very image obsessed culture where plastic surgery is more normalised and people get "fat shamed" on television so maybe adults calling one another fat and ugly like you would expect from 5 year olds is less noteworthy, idk.

I think it because he wears those baggy clothes at work, so it seems so, even if he is so thin. Also they are just being mean. ┗( T﹏T )┛
http://www.mangago.zone/read-manga/one_sided_love/mf/d_v-1-chapter-6/pg-26/