A nearby star having a near-transit of a galaxy will cause a time-dependent weak lensing of the galaxy. Because the effect is small, we refer to this as weak microlensing. This could provide a useful method to weigh low-mass stars and brown dwarfs. We examine the feasibility of measuring masses in this way and find that a star causes measurable weak microlensing in a galaxy even at 10 Einstein radii away. Of the order of 1 mag I <= 25 galaxy comes close enough to one or the other of the ~100 nearest stars per year.