Third year is best to begin harvesting even if you start out with plants that are supposedly "two years old". There will always be fat ones and skinny ones but fewer of the skinny, which you can snap off and put in the compost, eat raw or add to a salad.
A new neighbor dropped over, almost 20 years ago, and loved our asparagus patch but moaned about having to wait for years to eat them. I told her it's just a 12 x 12' area and she only had a huge field of grass behind her home so would she rather wait and have asparagus or have her husband mow it forever. She never planted any so still can't enjoy it fresh from the garden. I pick ours at 6:45 and we're eating them, roasted, at 7 PM.