What would be the best weight for lead sling projectiles? I have a 27 inch sling.

depends oh the definition of 'best' and what you want the lead projectiles to do.

Historically somewhere between 40-70 grams are commonly found on battlefields and at those weights they would have been primarily for distance slinging.
And also it meant you could carry a or more ammo.

If you consider a bombardment slinger will be easily throwing 10 shots a minute - quantity of ammo is really important.

now distance slinging with lead is somewhat problematical in the modern world.

Make damn sure you have clear vision for 500 metres. Lead projectiles are lethal - never forget that.

Apply similiar rules to slinging lead glandes as you would to using a firearm.

If you can't see where it's going - don't sling it.

What's a good/average weight for going for accuracy over distance?

Ich schieße gerne 50 g. Darunter mag ich nicht. Lieber etwas schwerer. Es gibt wenig Funde über 100g. Aber es gibt sie. Sogar 180 g.
50g ist ein gutes Gewicht.

Regarding Roman projectiles,
sometimes they have been found in sets that correlate with the Roman weights. Lightest type are ~1 Roman ounce (27.3g), ~2 Roman ounces for medium (~54.6g) and ~3 Roman ounces (81.9g) for the heavy type. There are also batches that correlate to fractions of these weights i.e 1.5oz, 2.5oz. etc. I don't think it's a coincidence.
Caches of even heavier ~3.5 oz (~95g) projectiles have also been found, but only in certain places. Due to the expedient and rough manufacture of Roman bullets, their weights are not very precise.
Nonetheless, the different weights would be for different purposes. If I was going for maximum accuracy, I think I'd chose the 3oz type, but I've only properly tested ~50g glandes.

Greek examples are, historically, surprisingly light, say around 30-40g

[I wrote late, I meant light]

Theres a wholesale pack of 1 1/2 oz fishing weights that are perfectly oval, i was thinking about trying those, ive heard that lead projectiles are more accurate cause theyre heavier

Nein

My best weight for lead glans have always been a hundred grams  best for accuracy and best for distance also a lot of fun vs car doors

BasedCrusader wrote on Dec 18^th, 2021 at 12:22am:

Theres a wholesale pack of 1 1/2 oz fishing weights that are perfectly oval, i was thinking about trying those, ive heard that lead projectiles are more accurate cause theyre heavier

Density not weight.
Density allows missiles to have less reaction to air resistance and wind than less dense objects.
So will fly straighter.

The glande shape, paired with the spin imparted by sling, means the missile travels point first, so on impact all the energy is concentrated at the point.
This allows small missiles to do more damage.

But accuracy is Always 100% down to the individual slinger.

Spheres are a better universal shape, but glandes do more damage for the same weight and the shape makes them fly further.
The combination means you can use small light missiles.
Which means you can carry more and they cost less to make.

But never confuse density with weight :-)
Two very different missile properties.

I prefer 100 and 120 gram lead balls. Very accurate and a lot of force behind it. Can't carry as many though.