You found an interesting phrase. It is not about 身=body nor 蓋(ふた)=lid of pots.
It means " You say things too straightforward, without euphemism. "
So here's 2 example conversations...
ex.1
A: きのうジムの会員になったんだ。I joined a gym yesterday. マッチョになって、モテモテさ!( I will become a big muscle man and all girls will crash on me!)
B:お金のむだだよ。it's waste of your money. ジムの新会員の半分以上がひと月以内にやめるって知ってる? Do you know more than half of new members quit gym within a month?
A: そんな身も蓋もないこと言うなよ。(Hey, don't say that. It's brutally straightforward!)
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ex.2
A:なんで、あんな いやなやつと つきあってるの? Why are you dating with such a jerk?
B:だって、彼って ちょうお金持ちなの。Because, he is so rich!
A:身も蓋もないなあ。(Oh no... you are too straightforward.)
Hope it helps. (-;