The Waikato side ran in five tries in Hamilton, leading 27-10 halftime, before pulling away late in the second half.
Weber and number eight Pita Gus Sowakula crossed in the final quarter to snuff out any chance of a comeback from the visitors.
Chiefs lock Brodie Retallick was happy with his side's outstanding peformance.
"That was just a great Chiefs' pack performance," Retallick said.
"We knew the Waratahs led the statistics around the ruck and the breakdown so we knew we had to be tough there."