A "weak handshake" refers to a handshake that feels limp or lacking in strength. It is often seen as a sign of someone's lack of confidence or assertiveness. Full definition
Weak handshakes signal that you lack authority and confidence, while a handshake that is too strong could be perceived as an aggressive attempt at domination, which is just as bad. (entrepreneur.com)
Poor eye contact, a weak handshake, and bad posture can all send the message that you don't believe in yourself. (inc.com)
It's common for people to associate a weak handshake with a lack of confidence and an overall lackadaisical attitude. (businessinsider.com)