HelpfulGardener.com

My zucchini seedlings are approx 2-3 weeks old and are 4-6 inches tall. They have almost all fallen over. Other than that they still look healthy. They are a nice green, seem strong and are now sprouting first set of true leaves. Just yesterday I put a grow light on them overnight thinking that the problem was lack of light because of the weather lately and have not seen much if any improvement yet. Is this normal? If not, what do I do?

That's what they do! Zucchini are vines that crawl and sprawl, unless they have a trellis to climb....

That is a problem growing squash, pumpkins etc without full sunlight.
They will grow like a bean stalk searching for sunlight.
Put some dirt around the stem to support them until you put them outside.
When you put them outside put the whole plant in the ground right up to the leaves and it will be fine when it get's the proper sunlight.

Mound up some soil for them.
The mounded soil will stay warm.