This is definitely too little light. Are you indoors? A greenhouse? No they aren't ready to be transplanted. If they are indoors by a window that is just not enough for light. You need to get a real grow light to start plants indoors. Those seedlings will strengthen if you get a real grow light. We've got lots of info on lighting on our site.
That window is just not enough light. As long as the temp is below 90 degrees F plants will do just fine.
If your plants have never been in the sun you will have to acclimate your starts to the sun before they ever feel sunlight on their leaves. Otherwise they will burn. Acclimating thickens the epidermis to protect the other cells from the radiation of the sun. Sort of like our melanocytes. Lots of answers about that as well on our site.
If you have a covered patio or deck I would definitely put them out of doors. What are the night time temps? Good time to start if you want to transplant in your garden.
I also rip that thin fabric off, or cut it off before transplanting. I usually up pot into a 4" first, allow roots to fill and make sure the starts are used to the amount of light, wind before planting in the prepared beds of the garden.
Have you used fertilizer? That might also be why they are so elongated. Fertilizer helping them grow when they are unable to make enough food for themselves causes plants to elongate and thin leaves in an effort to reach more light. Don't fertilize until planted in 4" pots. Sparingly.
Hopefully you are using bagged potting soil. Growing in pots one has to use potting soil. They will be just fine transplanted into the garden soil.