Small Spiders will quickly run toward Albert West on sight, and bite him rapidly. Their attacks slow West a bit when they hit, so even a small group of two or three spiders can lock down West if he gets hit. Shielding the hits or dodging back are almost necessary to escape if West is caught.
Small spiders only attack with melee, so retaliating with your own melee will suffice, and is actually recommended since it can be difficult to hit them with guns. If there are too many spiders around, a photon grenade can easily clear them out. If they are spread out sufficiently, a lucky shotgun shot can clear them, but the power required may not be worth it.