It throws up a flower spike which eventually opens to look like the link.

FataMorgana

Here is a link that might be useful: Google Images - Dill Flower

I've seen the pics on Google before, but didn't know if they started out looking the same as your normal leaf stalks or if there was a differentiating feature.
Also, I've seen it before that you can cut the plant to the ground and it will come back. Any experience with this? I feel like the plants are getting way too tall and flimsy.

The flower spike is a thicker stalk that comes up from the center. It's obvious the plant is doing something other than continuing to make the fern-like leaves.

I've never tried cutting it to the ground. I've got my doubts about that working out well. If grown outside, dill doesn't get too tall and flimsy until perhaps the seed heads get too heavy but the plant is at the end of its life then. Are you growing these indoors?

FataMorgana

They were indoors for the majority of their lives. But now that they are so tall, they outgrew my single plant light stand. And if I left them under the fluorescent lights it would require moving the light too far from my other plants. Plus we've had a really mild winter here in west Florida, so I've moved them outdoors now.

If they are that tall and flimsy, I might try staking them.

Of course if your temperatures are that mild - as it has been here in the usually frozen North, try sowing some seeds in a pot or direct-sown into the ground outdoors. According to what Dr. Google has to tell me, dill needs at least 60 degrees F to germinate.

FataMorgana

Yes you can cut it back leaving 3-4" . You can also do the same with fennel too. I do this often to get new growth for the black swallowtail butterflies.