First, It's better to give plants a good deep soaking once a week, than a little bit of water everyday. Most vegetables need an average of one inch of water per week. RAIN is the best source. What you give from the hose is only to supplement the rain. Get a rain gauage and keep track of how much you are receiving. It will give you more confidence until you get a feel for what your garden plants need. Also, before you turn on the hose, stick your finger into the soil about an inch deep. Then rub your finger and thumb together. If you can feel moisture, your plants don't need water. If you can't, they do. It's not a bad idea to mulch your beds to conserve moisture.

Five to six hours of sunlight is a bare minimum. This probably has something to do with your slower growth rate.
On the other hand, three weeks isn't a long time. Be patient. :)

Most plants grown from seeds, will concentrate on growing and developing
root system early on. That is one reason why you do not feel they are growing
as fast. Soil temperature, air temperature , nutrient and water are other factors.

My summer vegetable seeds are growing slowly too. We have been having some very cool weather in our zone here, which I attribute to the seeds slow growth.

Peas and radishes won't mind, but cucumber and corn are probably wanting a bit more heat. As donnabaskets says, "be patient."

Bejay

Bejay gives pretty good advice for So Cal gardeners, so you can't go too wrong listening to him. Partial shade here can be like other people's full sun, and full sun can be like a blast furnace.

As for overhead watering, that's all I ever see around here commercially. The remaining large plot growers all use large sprinkler systems, rainbirds and the like. The nurseries that I go to all overhead water. I don't have time to sit and watch/manage a series of soaker hoses and such myself. I have used overhead spray from a hose nozzle for many years -- and during some hot spells I do water almost every day. If you wait for rain around here, or follow some kind of calculation, you will not have a garden for long. The trick is to not let the wilting of plants fool you into watering too much. Sometimes well watered plants will wilt like they are on death's door because of the intense/direct heat. Let the soil be your guide.

Keep the soil evenly moist and you'll do fine. Layers of newspaper or cardboard and then a layer of mulch on top will help cut down on watering.

Also, I don't plant the warm season garden until after St Patrick's Day. Warm season plants will just sit and sulk if you plant them out too soon. Still haven't planted beans and cukes yet as some mornings are still under 50*.

And just so you know...I was having the same issues too until we ran into a warm spell and then...POW...everything kicked into high gear and I could swear that my tomatoes are growing inches per day. My cucumbers were doing absolutely nothing one day, and within a couple of days, I had three little baby cukes growing. All in due time.

Thanks for all the great advice! I guess I will just have to be patient.

As far as sticking my finger in and only watering when it's dry to that point, does this go for seedling size plants too? Or should I keep those more moist?

Thanks!