1. To offer (someone) a proper or formal expression of greeting, welcome, esteem, or well wishes. I think we should go over and pay our respects to the new neighbors and make them feel welcome to the area!
2. To offer or express one's condolences or sympathy, particularly to someone's family following his or her death. I'm heading to Janet's house after her father's funeral on Sunday to pay my respects to her and her family.