Dill, like most any plant will not suddenly get used to being outside and direct sunlight. Because yours are in small pots, they must remain there, as dill does not transplant well. They will lean and fall over as they are quite young. I moved (was always outside) a single dill plant two weeks ago, that was 12 inches tall. Its still wilted and has not recovered the transplant. If you have a garden, its much better to directly plant dill seeds outside. Mine go to seed and sprout MANY new plants the following spring even in Z6. Its everywhere it was last year and then some.

Ok,

But then, I don't understand why so much persons start their plants inside during spring, then transplant it outside in the beginning of summer....

It's not a good idea at all?!

snorky: Your dill still looks extremely healthy to me. Dill always does that leaning, usually until it's about a foot tall or more.

Not all plants need the indoor starting before going outside. It does make sense for things like tomatoes, and other longer maturing items to start then indoors. The dill is quite hardy and will not start to sprout from seeds until weather is warm enough for them to germinate in spring. Same with cilantro. Some herbs like basil, thyme, oregano and others do need more time indoors before planting outside. I think yours just got shocked from the direct exposure to sun. When I put my plants out in my greenhouse in early May, they get hardened off there before being planted. If I started the plants indoors in March, then transplanted them directly in the garden, half would probaly die of sun scall, or shock from the soil changes and variable temps. Give the dill plants a couple of weeks and they should recover, but still may lay sideways. The reason is simple, most plants always do better when growing outside directly. I had a tomato plant show up next to my compost pile. It was from the year before and a small tomato must have survived the cold winter. I saw it start to grow in about mid May, but it never got passed a golf ball size tomato and was killed by the first frost of fall. Dill stalks are quite fragile and can snap in half if pushed too far.
Just remember, some plants need to be started indoors to get to a size where they can get transplanted outside after they get used to the direct sun, while other seeds and survive a winter and will start to sprout in spring. My cukes have just been planted and its going to be a race as to weatehr the dill is mature before the cukes. Usually I get at the tail end of the dill and then cukes start to come in.

How! Thank you very much for all of your answers!

I understand now both the cause and what I should do.
You were very interesting to read.

Thanks a lot!

I've had a number of plants knocked flat by the harshness of the sun when I first put them outdoors. I rummaged around in the shed and found some old window screens from my storm windows to place over the plants and it eased their distress. Stacked up to three on really sunny days and reduced the number to zero as they adjusted.

What your doing is simply 'hardening off' the plants. This is usually done with all seedlings tarted indoors and are headed for the garden. I have a small greenhouse and my plants stay there a week or two before they get transplanted.

I have always planted my dill in doors in March and I have had not prolbems with it growing great out doors. I was just concerned if I would be putting it out to early this year as my growing room is becoming over crowed.