Our plane has number 6 miniature nutplates (MK1000-06). There are so many of them that the weight difference probably does add up. Generally, here is the sequence I use:
Drill the primary screw hole to match the pilot on the nutplate jig - this could be a 6 or not, depending on which jig you buy.
Use the jig to drill one leg side to a #40 hole. In a pinch, a nutplate can serve as a jig, but it means having to start a screw in the nutplate. Also, if I use a nutplate as the jig, I only use it once, then install it. If you keep using the same nutplate over and over again, it will get a little wallowed out.
Flip the jig and drill the other side - if you are using a nutplate as the jig, stick a cleco in that first hole.
Drill the center hole to final size - if it is a #6 jig and a #6 screw, I usually upsize the aluminum hole to a #8. Otherwise, the aluminum gets in the way.
Debur all three holes
Create the countersink or dimple as applicable
Cleco one side of the nutplate
Rivet the other, then remove the cleco and rivet the final hole.
Naturally I'd batch these tasks and not do them in order for each nutplate, but rather do a whole panel's worth of each step.