Why Reynaldo was asked to find out about Polonius son
Polonius was seemingly over-officious thus never left anything to chance. He has demonstrated his servant ship to Claudius which great strength in punctilio. From this, he wants to ascertain that his son is not doing anything that could let him harm himself, or in some other context wants to make sure that if Laertes is coddling in such behavior, Polonius should be the first to know it. This is clear since even at the moment when Reynaldo seeks to know why Reynaldo is spying on Laertes, He responds in a manner that depicts him as a funny character who cannot even make up an excuse.
The other justification is perceiving Polonius as a political intriguer and manipulator. That he uses a spy on his son which reveals so much about his character and how he even doubts those within his closer circle. It also prepares the audience for his role in going to extremes of using his daughter as bait to bring out the true reasons for Hamlet’s madness. Such words cannot come from a doddery man but from a man who is dangerous and with a calculating mind who on a personal level is not interested in presenting himself as innocent only to murky is much dangerous self.