It's time to move them to bigger pots (5" ones) because they are beginning to outgrow the little 3" ones.
Comparison of tomato plants in 5" and 3" pots
I think it is important to do this so-called "potting-on" at the right time, because if the plants remain in small pots for too long their roots can become overcrowded, which in turn adversely affects their development. On the Down side though is the fact that once they go into the bigger pots it becomes much more difficult to protect them (or bring them indoors) if the weather turns cold again, which is entirely possible. Frost in the first half of May is not uncommon here.
There's not a lot for me to say about the actual mechanics of potting-on. I think perhaps the best advice I can give is to water the plants an hour or so before doing the job, so that their compost is thoroughly moist. Then when you are ready you can turn each little pot upside down and give it a sharp tap, which will hopefully release the plant and its compost all together. If you can keep the rootball intact this will be much less stressful for the plant.
When the young plants are in their new homes it may be advantageous to water them again, to help settle them in. Also, place them in a shady position for a few hours to help them recover from "transplant shock". Don't forget to label them!
The potting-on task gives me another opportunity to select the best plants, and weed-out any that are not up to scratch. As it happens, this year ALL my plants are good enough to keep, but I only potted-on 30 of them - simply for space reasons. That's the number that I can fit into the gravel-trays which I use for moving the pots around the garden. Once I'm satisfied that the ones I transplanted are happily settled in their new pots, I'll give the remaining plants away.
In the black pots are Mint cuttings.
Eventually I plan to have 12 "big" tomato plants, grown as tall cordons, which I will grow in 35-litre pots, and 8 (possibly 10) bush-type ones, which will be grown in smaller containers. I say "possibly 10" because when a couple of the Maskotkas failed to germinate I sowed some more, and these are presently a long way behind in terms of development. By the time they are big enough to be useful they may find that all the available space has been used!