I have a tip! 뚱 sounds like a big round fat ball bouncing and 똑 almost sounds like "doc", which is short for "doctor", which are pretty smart people! 의사가 똑똑합니다 -> The doctor is smart.
Here we contrast the verb 하다 with 지만 right? But how does that is seen as "but"?
No, 하지만 as a whole is seen as "but" here. It can also attach to a verb and retain the 하 : "저 남자는 똑똑하지만 멋이 없어요." (That man is smart, but he's not cool.)
It is used by itself as 하지만 all the time to mean "but/however", that's what matters
As a side note, don't start using "하지만" all the time in spoken Korean. I did, until my friend asked me to stop and use the more colloquial "근대".