Meaning
A pain in the neck / An annoying person
Example
Eu não quero que Marcos vá conosco, ele é um mala sem alça!
I don't want Marcos to come with us, he's such a pain in the neck!
Origin
The expression works through pure imagery and has no documented historical origin. A mala (suitcase) is already heavy and awkward to carry; a mala sem alça, "a suitcase without a handle," is even worse — there is no good way to grip it, so it becomes a burden you can barely stand to lug around.
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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