That is a matter of using the right tuners. There are plenty lightweight tuners on the market.
I have built several 12-string bass guitars. And none of them suffer neck dive.
I use Gotoh Res-o-lite bass tuners. And Gotoh Stealth tuners for the octaves.
Because I kept getting comments from people who were sure my twelve strings bass builds would be one big neck dive fest, I did a little slap-stick in one of my demo videos: