Seems kinda early for apples to have much size especially in a "cool" zone. Fuji in particular doesn't get ripe until October. Also final size is highly dependent on growing conditions and amount of fruit left on the tree.

Here is what I did with my trees. I transplanted them and let 3 seasons go by not allowing any fruit production in order to use the energy to grow a solid tree. I never fertilize, I have good soil and just let nature go at it's own pace. Each year I pruned away 1/3 of new growth on desirable branches so that the branches would be stronger when they do bear. Now that they do fruit I thin to the distance of pinky-tip to thumb-tip spread as far apart as possible. I grow nice big apples this way. Also first fruiting year, I allowed only 6 apples per tree.

I don't know if there is anything applicable you can glean from that, but hopefully it will help someone

Had a Anna & Fuji in So. Cal
Remove some of the fruit -Med. size trees should only have a few apples per branch. It could also be a water issue are you watering enough?

Anna will produce 2 crops a year in SoCal.
I always removed the 2nd crop (this one overwinters) because they never matched the higher quality of the first crop.

Jean
who gardened in LB, CA, for 30-some years

I agree that it is too early for Anna's to be ready to eat, although I don't remember what month I usually harvest mine. Right now mine are about the same size as yours. If you want larger fruit you can thin them. As to when they're ready, it partly depends on whether you like your apples a bit tart, or sweeter but a bit softer. I'd watch the color. If the Anna's are all green it is definitely too early. They will turn a much lighter green, then get a blush of red. Eventually they lose all the green color but I prefer them before that point.

As far as I recall -- and that's a struggle after 20 years! -- Anna ripens in Sept or Oct.