People talk about bullet weight because it's convenient, but the twist / spin rate requirement is not a function of the weight of the bullet, but rather the length, weight distribution and bullet shape. "62 gr" trips the alarm bells because 62gr M855 is not a traditional lead core bullet.
A 62gr lead core flat base is very different in stability from a 62gr M855, partial steel core boattail.
This is why the copper monolithic bullets are difficult to judge, for a given weight they're much longer than a traditional lead core jacketed bullet.
Weather conditions also change stability, colder air is denser and increases the need for stability... so a combination that is marginal in hot weather may fall apart in cold temperatures. Then again if you're not dealing with any cold environments you might not worry about having extra stability to handle a weather extreme.
A longer barrel increases velocity which increases spin rate, but also increases aerodynamic forces on the bullet so the net increase in stability is pretty small.
The 1:9 barrel is a relic of institutional inertia from the 1980s and was intended for M855 and the derivatives of that bullet type like the 68 & 69 grain OTMs, which at the time were the longest bullets commonly available. When the 75 & 77 grain OTMs came on the market, a few 1:8.5 barrels were made but this should have become the industry standard. A 1:8.5 will shoot any standard ammo that will fit in a magazine in reasonable weather conditions. But AFAIK no one makes that twist anymore. It was rapidly replaced by the 1:8 in competition use with the advent of the very long 80 grain Sierra OTM, used single-loaded since it's longer than magazine length and needs the faster 1:8 twist.
Quoted:
Will 62gr work fine in a 1:9?
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If you mean M855, then 1:9 is the ideal twist rate according to the traditional rules of thumb.
If you have a 1:9, the 75 and 77gr OTM type bullets will likely be marginal at best, and probably best avoided. The Berger 73gr OTM is supposedly ok in a 1:9, at least in reasonable temperatures. 69 & 68gr OTMs are good.