Asparagus, new to me

spindly spears could be any number of reasons:

1) crowns are still young
2) self seeded plants that are still young
3) soil not fertile enough
4) soil too compacted so roots not able to spread out
5) plants too close together so competing for resources
6) roots damaged (especially if close to the surface and someone has been a bit heavy handed with the hoe)

If planting spaces are fine and you've ruled out self seeding and root damage, then I'd just harvest the fat ones and leave the thin ones to grow on (they'll feed the crown while you keep on harvesting)  Add compost/manure to the bed every year to improve soil fertility.

Basically stop picking about late June so that the later foliage can grow and allow the crown to recover.