It took 19 minutes for Weber to open Waikato's account after Declan O'Donnell burst through a gap and set the halfback away, but from there the floodgates opened, with Michael Mayhew crashing over two minutes later to make it a 14-3 advantage.
Waikato were offloading at will in a grand display of free-running rugby, and crossed for a third try right before halftime as McKenzie broke through the first line of defence before freeing Weber, who cut inside the fullback to go under the posts for his second try of the contest.
The tries kept coming after the break, with a fantastic Tucker offload letting Jordan Payne saunter over in the corner, while Zane Kapeli notched his first ITM Cup try to stretch the lead out to 36-3.
Bay of Plenty managed to get a consolation try through Joe Tupe, but the encounter finished on a deserving note when the dominant Tucker got on the end of a backline play to snare a try for his standout efforts.
Waikato now return home to take on Auckland, while Bay of Plenty will travel to Pukekohe to meet Counties Manukau.
Waikato 43 (B.Weber 2, M.Mayhew, J.Payne, Z.Kapeli, J.Tucker tries; D.McKenzie pen, 5 con)
Bay of Plenty 10 (J.Tupe try; D.Hollinshead pen, con)
Halftime: 24-3