Caterpillars and lady bug larvae love it! They use the plant for a food source and for laying their eggs. Since they prefer it to other plants in my garden sacrificing the dill saves other plants in the garden I much prefer in a more pristine state.
The bugs get a healthy plant to complete their life cycle and I get butterflies and lady bugs throughout the summer. Bonus, the dill reseeds itself each year. It's not invasive at all. If it reseeds in the grass you can just run the mower over it. Double bonus, if I'm careful and quick about it I can gently stroke a caterpillar's head.
As someone who's terrified of bugs that's pretty bold for me. If you aren't going dill in your garden you should consider it. Its an organic way to help your garden stay in balance, remain healthy and who doesn't want butterflies flitting around among your flowers?
[Correction: There were a few lady bug larvae on the dill but the ones pictured here developed into caterpillars instead. Couldn't get a decent shot of the lady bug ones.]