You will likely need to collect and re-check. Also, NZ's weight limit is 23kg not 24kg.

As for your allowance, what does your ticket say? For interline journeys, many airlines now display comprehensive allowance information somewhere on the ticket due to US DOT rules (it was easier to apply the information requirements across all tickets rather than just ones which touched the US).

Does the NZ flight have a scheduled departure time within 24 hours of your AC flight's scheduled arrival time? Same-ticket flights within 24 hours of one another are generally considered by the industry as "connections" or "transits" - even when you need to collect luggage, clear customs, and re-check etc. So, despite your overnight in YVR, if the NZ flight departs within 24 hours of your AC arrival, it's likely that AC's allowance will be applied to it (due to IATA's Most Significant Carrier rules).

However, if NZ's allowance applies to your YVR-AKL flight, assuming you have Star Alliance Gold status, you will be entitled to 4x 23kg bags. This is made up of the Business Class 3x 23kg allowance + 1x 23kg extra bag for being *G. This extra bag is permitted as your ticketed itinerary has 2 or more Star Alliance carriers. If your ticket was solely NZ-operated, it would be capped at 3x 23 bags with no additional *G allowance.