1. Sterilize jars, and prepare lids.
2. While jars are boiling, bring 2 cups water, vinegar, and next 4 ingredients to a boil in a 3-qt. stainless steel saucepan over medium-high heat, stirring until sugar and salt dissolve.
3. Rinse asparagus; snap off and discard tough ends of asparagus. Trim spears to 4-inch lengths (to fit jars). Place 2 dill sprigs and 1 garlic clove in each hot jar. Tightly pack asparagus, cut ends down, in jars, leaving 1/2-inch headspace. Cover with hot pickling liquid, leaving 1/2-inch headspace.
4. Seal and process jars, processing 10 minutes.
5. Remove jars from water, and let stand, undisturbed, at room temperature 24 hours. To check seals, remove the bands, and press down on the center of each lid. If the lid doesn't move, the jar is sealed. If the lid depresses and pops up again, the jar is not sealed. Store properly sealed jars in a cool, dark place up to 1 year. Refrigerate after opening.