Right, but if that were the case, and 100% of damage from both were based on the effective AP formula, then DPS output should be directly proportional to AP% per minute, and the marginal DPS value of weapon DPS should be proportional to AP% per minute. Which means if DPS were equal, so should the marginal value of weapon DPS.
But that’s consistently not the case.
Sims are used for stat weights specifically because they can handle this. Literally what sims do to calculate stat weights is run sims that incrementally increase the given stat while holding others constant, and calculate the average DPS gain per point added to said stat (and then repeat that process for each of the other stats). So procs would certainly be taken into account.
That said, you may be on to something with Dance of Death. That increases agility, with a fairly high uptime. The higher your agility (while holding weapon damage constant), the less of your effective AP comes from your weapon, and thus the less marginal value relative to your total DPS comes from increased weapon DPS.
MM’s traits largely revolve around either static damage adds (Surging Shots, Focused Fire, etc), or secondary stat buffs (In the Rhythm), so MM’s weapon stat weights wouldn’t be being depressed the same way.
That all said, I still don’t see it making the difference it does atm. For example, here’s my hunter simmed for BM, and then simmed for MM (and only having one of his 3 Azerite with MM traits, too, so overall DPS is much lower):
https://www.raidbots.com/simbot/report/bier5C6kjbBiJx68YHP59G
https://www.raidbots.com/simbot/report/bwRpD2guGNB9KkdHfq44rq
Even with the simmed MM DPS being 21.5% lower, his marginal value for weapon DPS is 60.5% higher. That means that, if he were doing equal DPS (and the contribution scaled proportionally, which is likely), his MM weapon damage weight would be slightly more than double.
So something is definitely going on here. MM is scaling substantially better with weapon damage, according to the sims, which says to me a substantial portion of BM’s damage is not scaling the same way with weapon damage.