Meaning
To turn a blind eye
Example
Vi um homem escondendo uma cerveja dentro do casaco... tive que fazer vista grossa.
I saw a man hiding a beer inside his coat... I had to turn a blind eye.
Origin
Etymologists trace it to the idea of willingly 'making the eye thick' — pretending not to see clearly. 'Vista grossa' appears in 18th-century Portuguese texts with roughly the modern sense.
Source: Phrases.org.uk — turn a blind eye.
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More idioms
Acertar na moscaTo guess correctly / To hit the nail on the headAmigo da onçaA fake/false friendAndar na linhaTo toe the line / To behave properlyArmar um barracoTo cause a public sceneRodar a baianaTo cause a public scene / To go ballisticArrumar sarna pra se coçarTo ask for troubleArrastar as asasTo hit on someone / To flirtAbrir o jogoTo come clean / To open upArregaçar as mangasTo roll up one's sleeves / To get to workAgarrar com unhas e dentesTo hold on for dear life / To seize an opportunity