  We classify all finite linear spaces on at most 15 points admitting a
blocking set. There are no such spaces on 11 or fewer points, one on 12 points,
one on 13 points, two on 14 points, and five on 15 points. The proof makes
extensive use of the notion of the weight of a point in a 2-coloured finite
linear space, as well as the distinction between minimal and non-minimal
2-coloured finite linear spaces. We then use this classification to draw some
conclusions on two open problems on the 2-colouring of configurations of
points.
