Someone asked about the weight of Roman lead bullets. I can't find his post. So, I create this one to answer him.
On a French site dated about 100 before Christ, 14 were found.
The weights are between 30 to 85 grams.
The archeologists think the heaviest are for distance and the lighter ones are for short-range accuracy.

Shared by Archaic Arms in "Catch this" section.
http://av.zrc-sazu.si/pdf/62/AV_62_2011_Laharnar.pdf
More bullets ( a few sites in Slovenia) and almost identical weights.

Do you have details on the french publication (name, date, journal, title)?

I have read about Roman lead sling bullets in the range of 20 to 180 gram, with an estimated most likely weight of around 50 grams , with a tendency towards higher weights over the course of time

the site in French :
https://www.academia.edu/29469275/Des_balles_de_fronde_en_plomb_de_larm%C3%A9e_romaine_%C3%A0_Caylus_Puech_Boussac_Saint_Affrique_par_P_GRUAT_G_MARTY_et_J_POUJOL_CAA_N_16_2002

It also says that slings are simple leather straps. Ok, I test. Goat leather (very flexible and very thin : 1 mm), length : 1,20 m and width : 1,5 / 2 cm. No pouch, no fingerloop, no knot, nothing. First shot, a little apprehension and the bullet went rather to the right. Second shot, relaxed and a shot slightly above the target.
The target was about 30 meters. My style is underarm. The weight of the bullet was 50 grams. The trajectory was very flattened.

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TOMBELAINE wrote on Jan 31^st, 2023 at 11:32am:

The weights are between 30 to 85 grams. The archeologists think the heaviest are for distance and the lighter ones are for short-range accuracy.

It's funny because It's very likely the opposite was true. With a long sling, you will get maximum velocity with the lighter projectiles, which provides greater range and flatter trajectory at lower angles. At long range, hit probability is also less, so lighter bullets mean you can necessarily carry more of them. 
Heavier bullets on the other hand, are more accurate to use and can be used more effectively with shorter slings for closer ranges. it's intuitive that a heavy bullet is best used when hit probability is higher, which is usually at closer ranges.

It's pretty well known that the vast number of archaeologists do not have a clue as to how things like slings and bows/arrows and other weapons were actually used. 

I'll bet 9 out of 10 archaeologists who write learned papers about weapons of any kind have never actually used modern equivalents, and have no idea how they work or what they are capable of.   

The exception is the very small handful of modern "reenactment" archaeologists who are actually trying to see how things were "back in the day"...

I don't know if these archeologists are right or wrong.
Their arguments are based on the analysis of a battle during an excavation. During the attack on a fort, small bullets were found at the location of the attack, and large bullets in front of the second door as a bombardment shot. Soldiers could contribute their military expertise.