Weak-minded works two ways, and they are close but not the same. First, it can mean not very intelligent — slow to think, unable to understand much. This use is old, and today it sounds unkind and out of date; you may meet it in older books, where it was almost a medical label for people we would now describe quite differently. Kind speakers avoid it in this meaning. Second, and much more common now, it means easily persuaded: a weak-minded person believes whatever they are told, follows the crowd, is talked into things, cannot hold on to their own opinion. That is the sense you will meet in modern writing — 'only a weak-minded person would fall for that advert'. Both uses are insults; you never call yourself weak-minded except as a joke about, say, buying too much chocolate. Compare weak-willed: weak-willed is about not doing what you planned, weak-minded is about not thinking for yourself. They overlap, and people are not always careful about the difference.