An average glande weighs around 2 oz (some were haevier, some possibly lighter, but not by much) - or 8 to the pound.
So given a sensible amount to carry in a pouch/bag would be around 10 pounds. Say 80 on their person.
Given that slingers were often positioned behind the regular lines - it's a safe bet that there would have been wagons carrying extra sling ammo. Also their would definitely have been runners to replenish any used ammo (same goes for arrows).

Basically the answer is that a slinger would have as much ammo as possible :-)

a soldier - from whatever era - carries about 30 kg of kit. or 70lbs if you wish. this is as true today as it was in antiquity, because that's more or less all that a man can carry and still fight. i wouldn't suggest that a slinger could shoot 30kg of lead in a battle, but as a soldier he would still have to carry his sleeping bag, mess kit, cooking equipment, rations, possibly some sticks for a pallisade, pick axe or shovel, all or part of a tent, weapon, ammunition (or lead ingots) spare clothes socks and so forth. the fact of his weapon being light would allow him to carry more stuff in his kit.
so i wopuld guess that a slinger would carry the weight of his essentials, plus the weight of ammo or lead, which would bring him up to around 30kg. no bow, shield or armour would mean more glandes

SV            

someone had to carry the lead, iron pots, and fire-making kit - this could be carried on mules or wagons, and the ammunition was made on the spot. the question is, why?  no-one else using lead ammunition (musketeers, or even modern armies) cast their bullets on the spot - so why did the ancients?
maybe lead was too expensive and deadly to hand out as sling bullets, in case of desertion, and was cast on the day, and given to soldiers under supervision

SV

Yes, I know that lead glands where often moulded „on demand". That means when the soldiers knew there would be some clashes or a battle in the next hours or the next day. Probably it was simply easier to carry blocks of leads than a lot of little glands. A little gland would much easier fall from a waggon.

A Mongolian soldier had to prepare at least 60 arrows before any military expedition. If such an arrow weights 50g (the arrows of english longbows had a similar weight), 60 arrows weight 3kg. That is not so much and theoretically he did not even have to carry them himself as he was on a horse. On the other hand, the slinger is walking on his feet, a gland (or stone) is probably heavier than 50g and as the slinger makes more dynamic movements than a bowmen, a lot of weight hanging on his bodyside (whereas the arrows are on the back) would hinder him much more. So my thought was that in a battle a slinger would not have so much ammo with him. 60glands of 100g makes 6 kilos. When I go to slinging I usually carry a bucket with 40 plastic balls filled with sand, weighting 170g each. This gives „only" 6.8kg, say 7kg with the bucket. I could never sling with this weight hanging on my body ! It is really a lot. Perhaps the romans also used buckets... I think that 3 to 4 kg of ammo is the upper limit. This is 60 very light bullets or 30x100g bullets. Probably a 50g lead gland is much deadlier than a 50g stone, so they could still carry a lot of ammo when using lead glands. That is why I wanted to know what a typical gland weights.

Not sure on my facts on this one but didnt they use shot towers to make lead shot in 17th or 18 th century used by pouring molten lead through holes in the top of a tower into water a long way below.
could this also have hardened the lead as it cooled quickly on hitting the water, dont know if you can harden lead is the answer, should know Iv'e been an engineer all my life.

I remember reading in a guns and ammo casting article that pure lead can indeed be hardened by water. The bullets were heated in a separate operation, just below their melting point, and dropped into water. The tempering apparently exceeds linotype in hardness, however: the effect will reverse itself in a matter of weeks rendering the bullets softer than the original metal.

I just had to give it a try.  Slinging with a 10lb satchel (4.5kg, or approximately 45 100gm lead glands?) slung over one shoulder was no big deal.  Even a 20lb satchel didn't seem out of the question for a simple helicopter/overhead throw.

Shields were another matter.  Slinging with a 10lb shield on my left arm was pretty hopeless -- much harder than swinging a broadsword -- though I imagine it's a skill that could be learned with practice.