The more soil there is, the more nutrients your plant will have access to, meaning it will grow faster and you will not have to feed as early or as often.
You will also have much less chance of getting any sort of nutrient salts building up to toxic levels in bigger pots.
For photoperiod plants, I would certainly not consider anything under 5 gallons as being adequate.
Bigger pots will certainly benefit your plants.
And yes, more soil = more roots = more plant.
Also, remove the "humidity domes", your seedlings do not need them, but they do need good air exchange to sprout and grow properly, something that humidity domes prevent.
Humidity domes also increase the risk of disease and/or moulds and fungus, which can be fatal to young seedlings.
Just because "everyone else uses humidity domes", does not make it right.
Hope this helps, Organoman.