Anethum graveolens or dill refers to an aromatic annual herb that belongs to the family Apiaceae which also has carrots, celery, parsley, and other herbs. Dill is grown for its seed and leaves which are used as food flavorings or herbs, especially in Eurasia.
Nutritionally, dill weed (plant or leaves) has carbs, proteins, fats, vitamins (vitamin A, B1, B2, B3, B5, B6, B9, B12, C) as well as minerals including calcium, magnesium, iron, phosphorus, sodium, zinc, potassium, manganese and copper. All these are vital nutrients that bunnies need.
Can bunnies eat dill?
Yes. Rabbits can eat dill. It is one of the bunny safe herbs together with others such as basil, coriander, parsley, sage, thyme, mint, rosemary, and oregano. These fresh and moisty herb forms part of the leafy greens you can give your bunny and it will promote gut motility being fibrous.
However, due to the strong taste of most of these herbs, some rabbits may not like them at first and hence often listed as foods not much favored by this pet.  Nevertheless, with time, most bunnies will love them especially if they get used to them.
Whereas a source  states that you should not give your bunnies dill flowers or weed stating that they are very acidic, have high calcium and phosphorus levels and thus not safe, this is not the case. Dill is safe and it is listed as some of the leafy greens with low oxalic acid and its safety is not in doubt.  
On the issue of calcium amount, this herb has only 208mg of calcium per 100g while a medium size bunny requires about 510mg of calcium daily . Besides, your bunny needs one packed cup of chopped 4-6 leafy greens with dill being one of them, per a 2-pound weighing bunny.
The amount of dill will be small considering you mix with 4-5 other leafy greens. This is the same case with phosphorus. Therefore, when giving this herb to your bunnies, you can mix it with other leafy greens such as carrot tops, Mache, kales, Endive, cucumber leaves. Cilantro, Bok Choy, watercress, dandelion greens, wheat grass, and so on.
Furthermore, ensure it is free of pesticides and thoroughly wash it under running water before giving it to your furry friends.
Also, avoid pickled foods including pickled dill and start with small amounts as you see how your rabbit’s stomach will respond. If there are no stomach upsets, you can increase the amount to what we have recommended gradually over a week.
Stay away from seeds
Whereas the dill weed (flowers, stems,
Foods high in carbs and starches are associated with enteritis and obesity in rabbits. Therefore, do not give these seeds.
Giving your pet the right diet is very important in maintaining a healthy gut since their digestive system can best handle high fiber foods. Therefore, hay should be given in unlimited amounts, 10-15% fresh foods and about 5% be high fiber pellets.
Note that 75% of the fresh foods should be leafy greens with the remainder being small treats of non-leafy vegetables as well as occasional treats of fruits. Do not forget to give them an unlimited amount of clean, fresh water.