As been stated previously "define a precision hunting rig for you".
Every hunter has different needs based on both game & terrain. Weight becomes relevant only based on what each individual deems acceptable to their needs. Accuracy at the MOA or sub-MOA level is a matter of personal preference IMO & something that can be achieved through both practice & hand loading/fine tuning of the firearm.
The guy (or gal) thats on a multi-day Sheep/Goat/Elk hunt requires a light 6-7-1/2lb rig that can solidly & constantly anchor their quarry at range, but light enough that they can carry other essentials while on a backpack hunt. They really don't want the 9-11lb Varmint rig while they're hiking up and down slopes after spotting that trophy they just finished glassing for 2 days.
At the opposite end, most Varmint/Predator hunters are used to the typical 10-12lb rigs of their trade. Their stands are usually 30-60mins in length and then they move on to the next set. Precision here is based on small targets areas at up to long ranges using small calibers. Shot placement is a little more critical given the size of quarry & the small calibers getting knocked around in the wind.
Are the two above scenarios any different? Only by weight of the rig used basically, which again is based on game & terrain. However, each hunter is required to do their part regardless of the size of quarry involved.
Can a hunting rig become a precision rig? Yup, Jerry from Mystic Precision has proved that with his Axis Precision build/article.
Can a precision rig become a hunting rig? Absolutely, if you don't mind the weight it brings as a package, it's typical single feed factor or the big $$ involved behind these setups.
Anything is achievable depending on budget involved. At the end of the day, whether your using a 6-1/2lb Mountain rig, an 11lb Varmint rig or a 5-10k plus Precision rig all that matters is the person behind it is proficient enough to take game responsibly & humanely.
Just my .02 cents worth (probably 1/2 a cent worth after taxes

)