Do they have light? How do you water? fertilizer? Also, with seedlings a fan can help with providing some resistance, but as with hardening off, you want to go slow.

They get direct sun a little more than half the day. I planted them in those Jiffy peat pod trays and keep them damp but not soaked.

Your problem is most likely not enough light. Indoor seedlings need 14-18 hours of good light. Seedlings also need food if your starting mix does not provide it.

In my experience dill just doesnt have a sturdy base as a seedling. It will flop over, but as it grows it kind of props itself up from where it had flopped over, and grows up from there...

Thanks! I'll keep my fingers crossed. :-)

By 'direct sun' do you mean from a sunny window? That's not good enough for a sun loving plant. I also have concerns about the jiffy peat pellets, of that's what you used. They can provide great challenges; difficult to moderate moisture level.