How heavy can a dog-sized creature be with wings about 2-3 times its size?

Question

The creature I have in mind is more or less the size of a large dog (think Great Dane). It will have wings on its back similar to a dragon. Now I'm struggling with how heavy these creatures can be for it still be able to fly well.

I found the bird calculator which says that 60 pounds (27 kg) results in a wing span of about 3 metres. This is the wing span of an albatross, which only weighs about 12 kg. I understand that wing design and use (long flights, sprints etc) somehow tie into this equation as well.

What I'm looking for:

• Creature size of a Great Dane
• Wings like a dragon, about 2-3 times its length (more allowed if necessary, but wings should still be foldable. Are allowed to 'protrude' if they are longer than the body in folded state)
• Able to carry some extra items (about 5 kg)
• Still able to make sharp turns in flight

I'm looking for a way to balance weight, wing span/size & shape and flight speed (as a result of the first three) to match my ideas but keep it plausible.

Energy requirement is not an issue for this creature and is out of scope for this question.

Answer 1

Living creatures typically fall short of your creature's description, but I found the Quetzalcoatlus to be a rather interesting data point for you:

When it was first named as a new species in 1975, scientists estimated that the largest Quetzalcoatlus fossils came from an individual with a wingspan as large as 15.9 m (52 ft), choosing the middle of three extrapolations from the proportions of other pterosaurs that gave an estimate of 11 m, 15.5 m, and 21 m, respectively (36 ft, 50.85 ft, 68.9 ft). In 1981, further advanced studies lowered these estimates to 11–12 m (36–39 ft).

More recent estimates based on greater knowledge of azhdarchid proportions place its wingspan at 10–11 m (33–36 ft).

....

Weight estimates for giant azhdarchids are extremely problematic because no existing species share a similar size or body plan, and in consequence, published results vary widely. Generalized weight, based on some studies that have historically found extremely low weight estimates for Quetzalcoatlus, was as low as 70 kg (150 lb) for a 10 m (32 ft 10 in) individual. A majority of estimates published since the 2000s have been substantially higher, around 200–250 kg (440–550 lb).

Your bird calculator suggests a 500 pound bird should need a wingspan of 19 feet, which is roughly 6 meters. This suggests your calculator is not all that far off. It only predicts a little over half the wingspan of an existing dinosaur body plan. Presumably birds are a bit more efficient than dinosaurs were, so this isn't totally off the mark. That also lines up well with JBH's rough estimates in comments suggesting an answer between 3m and 9m.

Now there is one living flying creature with weights on par with this, which is the bustard. Kori bustard and great bustard are known to reach 40 pounds and wingspan of 2.7m (Kori bustard has unverified maximum weights that are much higher). Wikipedia claims:

The great bustard has a stately slow walk but tends to run when disturbed rather than fly. Running speeds have not been measured but adult females have been known to outrun red foxes (Vulpes vulpes), which can reach a trotting speed of 48 km/h (30 mph).[14][15] However, they can be fairly strong fliers as well, especially during seasonal movements, and can reach speeds of up to 80 km/h (50 mph) in flight.

I'll leave it up to you to decide whether their flight capabilities meet your creature's needs.