Mucho eazy to talk about bullet weight : twist rate . . . really, it's ALL about bullet length : twist rate.
For any bullet weight which a given jacket will accommodate, the mass is simply, "along for the ride".
For arguments sake, let's presume that all jackets are of BR quality - that is, maximum wall-thickness variation <0.0003".
Way back, to the beginnings of J4 jackets, and the decision to make 68 Gr. bullets using the .825" long jacket, none other than
Mike Walker wrote a letter, published in
PRECISION SHOOTING, admonishing the BR community, that is was/is a mistake to make a 68 Gr. bullet using this jacket length [combined with 1:14" twist] and expect the best precision.
Mr. Walker stated that the jacket should not exceed 0.810" long. In that era, the predominant jacket was the .810"Sierra, which featured(s) a radius base, as opposed to a flat base (J4), thus, once cored and flat-based, the .810" Sierra made/makes [about] the same finished bullet length as a .790" long J4 - around 0.815-.820" long. The .825" J4 jacket will run about 0.845-.850" long, roughly 1/32" longer.
"So, what" - they're both 68 gr. - right? To attain the same gyroscopic stability, the .030 - .035" longer bullet 68 GR. bullet demands a FULL 1.0" faster twist rate, or, 1:13".
Mr Walker believed we were smart enough to understand . . .
Instead, we entered the realm of constantly searching for the highest level of precision with a marginal/mismatched platform. The HUMMER concept, already born, was baptized - buy a dozen barrels and get one HUMMER - and to this day, people adhere to Einstein's definition of insanity: keep doing the same thing and expect a different result.

Every dozen barrels, or so, one gets a [so called] Hummer
*.
Or, do some homework and simply obtain the correct twist rate for the bullet(s) you intend to use. Regardless of your favored barrel maker, you'll be pleased with the much improved
Hummer to BUMMER ratio.
6mm, FB bullet, >.840" long: 1:13" (Sg 1.4), or, faster.
Or, use shorter jacket*. Pretty straightforward - Mike Walker was, "spot on". RG