How large, referring to weight, could a Dandelion seed become before the wind was no longer able to carry them away? Assume the physiology of both the seed and plant remain the same besides being scaled up in size. Also assume that the wind must be able to carry them under "normal" weather conditions with things such as gusts and breezes and discounting things such as tornadoes.
1000 dandelion seeds weigh around 0.8g. The size of each seed is approximately 8mm x 8mm by 10mm of a typical seed.
= 0.008x0.008x0.01 ie. 0.0000008 kg in 0.00000064 m3
weight of air in 0.00000064 m3 = 0.000000784 (difference of 0.000000016kg)
This gives a density of 1.25 kg/m3. The density of air is about 1.225 kg/m3. So you can see that it is only ever so slightly denser than air, and so the slightest gust can easily carry its weight.
Light wind gusts in an average city measures around 5 m/hr or 2.24 m/s. This is 6.1N/m2. Assuming this is vertical, and distributed over the cross sectional area of a seed (0.000064m2), this is 1.74m/s/s over that of gravity. As the size increases, the weight increases too, however the cross-sectional area only increases differently.
As an example at twice the size but same density, the seed weighs 0.0000032kg (double), and wind over crossectional area increases to 0.000128m2, giving a only a 0.12m/s/s over gravity.
So a typical dandelion seed can only be approximately 2.5 times as large before it becomes weight neutral in the same light 5mph gust of wind, and this may be the cause of its size limit in nature. Of course, stronger winds would lift it as it gets larger, and it is not unheard of for gusts to be much stronger, but you can see the principle (this is called the Square Cubed law, which explains that an Airbus A380's wings are much proportionally larger to a lighter aircraft, such as a Boeing 777).
In order for large dandelion seeds to be possible the density needs to decrease as size increases. This could be achieved by less but longer 'threads' to lift seeds, but you need to keep the volume up, so the threads need to be stronger. Basically you need a material that is stiffer but longer for fewer threads, the larger the size of the dandelion grows.
Eventually you may get something like 'silk' - a very strong material, over a long length, like a spider 'ballooning' thread.