Remy: Thompson seedless are naturally small berries. What you are seeing is somewhere near the normal berry size of that cultivar. Commercial growers achieve larger berries by spraying gibberellic acid to first thin the fruit off each cluster and then to plump up the remaining berries. They also use other tricks like girdling the trunk. You could do this. It's not that hard. But it doesn't increase the flavor or sweetness and may do the opposite. Doing a better job of pruning, thinning, and other cultural tasks can increase berry size somewhat if they are limiting factors. Commercially berry size increase is used only for Thompsons destined for table grape use or other special applications like Jumbo raisins. The normal raisins are grown with small berries just like yours. So the vast majority of Thompsons are grown like yours with small berries.

King of the North is a variety I'm thinking about trying here in the UK, it sounds very promising. King of the North is part Vitis riparia and according to Lon Rombough the small berry size is dominant in Vitis riparia and hybrids from it. From what I've read about King of the North, the berries are described as 'small to medium'. You could probably make the fruits a bit larger by girdling or using gibberelic acid, but I don't think they're really techniques for home growers. A simpler method is to thin some of the crop - if you remove some clusters before the begin to develop, then what remains will be slightly larger in size. I know this is an old thread, but if you read this, let me know how King of the North did for you.

I would suggest you ask on the Fruits and Orchards Forum where the keen fruit people hang out. It's much livelier than this forum and specialists will be able to help. Here is a link that might be useful: Fruit and Orchards Forum

Where are you located? Grape vines here live for many decades and never die back to the ground! But they do need consistent pruning each late winter or early spring. A 3 year old vine is not a particularly "young" plant and should be ready to bear now. Your grape was likely already at least a year old when you purchased and planted it maybe even older. The first year in the ground you need to remove flower/fruit to allow proper establishment and the development of the root system. And the second year, it may or may not produce any flowers or fruit anyway. By year three (at least a 4 y.o. vine) you can let it fruit but do not let it produce heavily. Thin out the clusters so that each has 12-18 leaves supporting it or roughly each cluster about 18-24" apart.