The part about the lighter equipment was a little bit of speculation on my part, but often a particular piece of equipment will be specced and put in the weight estimate, then another piece of heavier equipment gets bought for cheaper and installed. Not usually a big deal as the yard has a build margin to account for that, but if you don't carefully keep track, it can spiral out of control and the yard burns up the build margin and starts eating away at the EOSL margin.
Since, as far as I'm aware, there wasn't a proper weight management program, it's hard to say exactly where they went wrong. Another possibility for added weight includes using heavier plate (it's acceptable to do things like use 12mm plate in place of 10mm if you happen to have some extra lying around), but again, you need to keep careful track to make sure you don't end up with too much weight added.
Modern ship production design uses 3D modeling quite extensively, so every bracket, every bit of plate, every pipe spool, valve, etc. gets modeled and included in the weight estimate. It's pretty hard to be a long way off on the weight estimate if the ship is built to print. On the other hand, it's easy to add a few tonnes here with a budget oily water separator and a few tonnes there with a cheaper gearbox and end up with a ship that doesn't match the weight estimate anymore.
In the abscence (hopefully) of any other major flaws with the ship, this one should be quite manageable and won't restrict the operation of the ship. Basically, it means that the buck for careful weight monitoring has been passed from the yard to the RNZN.