The anomalous scaling behavior of the topological susceptibility ${\ensuremath{\chi}}_{t}$ in two-dimensional $C{P}^{N\ensuremath{-}1}$ sigma models for $N\ensuremath{\le}3$ is studied using the overlap Dirac operator construction of the lattice topological charge density. The divergence of ${\ensuremath{\chi}}_{t}$ in these models is traced to the presence of small instantons with a radius of order $a(=\mathrm{\text{lattice spacing}})$, which are directly observed on the lattice. The observation of these small instantons provides detailed confirmation of L\"uscher's argument that such short-distance excitations, with quantized topological charge, should be the dominant topological fluctuations in $C{P}^{1}$ and $C{P}^{2}$, leading to a divergent topological susceptibility in the continuum limit. For the $C{P}^{N\ensuremath{-}1}$ models with $N>3$ the topological susceptibility is observed to scale properly with the mass gap. These larger $N$ models are not dominated by instantons, but rather by coherent, one-dimensional regions of topological charge which can be interpreted as domain wall or Wilson line excitations and are analogous to D-brane or ``Wilson bag'' excitations in QCD. In Lorentz gauge, the small instantons and Wilson line excitations can be described, respectively, in terms of poles and cuts of an analytic gauge potential.