Cut the asparagus to fit the length of whatever jars you're using, leaving 1/4 inch headspace from the top of the jar. Pack the asparagus into the jars as tightly as you can. Tuck some fresh dill weed in between the asparagus.
To make the brine, place all the brine ingredients in a medium saucepan and bring to a boil. Boil for 3 minutes.
Pour the hot brine into sterilized jars, making sure to get some of the seeds and garlic in each jar, and leaving 1/4 inch headspace from the tops of the jars. Screw the lids on. Once the jars have cooled, refrigerate them for at least a week before eating. Will keep in the fridge for at least a month.
NOTE: If you really want to can these for long-term storage, immediately after pouring in the hot liquid and sealing the jars, process the jars in a water bath canner for 10 minutes. Remove the jars and let them sit undisturbed for 24 hours before moving them. Will keep for up to a year. Note that canning the asparagus will make them less crispy. Choose thicker asparagus.