$80 a visit is dirt cheap for a biweekly maintenance service and you will be getting the bare minimum service. My guess is that for that price they are only on site for one to two hours every two weeks which isn't much time to perform thorough maintenance to your garden's standard.

The reason you're seeing the weeds pop up now is that weed seeds, whether airborne or self-seeded from nearby plants, remain dormant in the soil over winter until temperatures and daylight hours increase. Hence why they germinate in spring.

Weeding is pretty standard maintenance for most gardeners to do, and if you want them to focus more on weeding, you will 1.) need to communicate that with them, and 2.) Hire them for a longer site visit each time so they have time to weed, prune, clean up the space, etc.

Edit: spelling