Recent speaker extraction methods using deep non-linear spatial filtering perform exceptionally well when the target direction is known and stationary. However, spatially dynamic scenarios are considerably more challenging due to time-varying spatial features and arising ambiguities, e.g. when moving speakers cross. While in a static scenario it may be easy for a user to point to the target's direction, manually tracking a moving speaker is impractical. Instead of relying on accurate time-dependent directional cues, which we refer to as strong guidance, in this paper we propose a weakly guided extraction method solely depending on the target's initial position to cope with spatial dynamic scenarios. By incorporating our own deep tracking algorithm and developing a joint training strategy on a synthetic dataset, we demonstrate the proficiency of our approach in resolving spatial ambiguities and even outperform a mismatched, but strongly guided extraction method.