When weeding in clay soil, we should consider using a digging stick or trowel to break the roots of the weeds.  It is easy to remove small weeds with these tools.
Weeds have different root systems and the weeds that grow close together may have their roots intertwined.  If you are using a hand trowel, you can dig down several inches and break the roots of the weeds with the trowel.  This will leave some of the weed roots intact, which makes it easier to pull out.