  Excitons in atomically-thin semiconductors necessarily lie close to a
surface, and therefore their properties are expected to be strongly influenced
by the surrounding dielectric environment. However, systematic studies
exploring this role are challenging, in part because the most readily
accessible exciton parameter -- the exciton's optical transition energy -- is
largely \textit{un}affected by the surrounding medium. Here we show that the
role of the dielectric environment is revealed through its systematic influence
on the \textit{size} of the exciton, which can be directly measured via the
diamagnetic shift of the exciton transition in high magnetic fields. Using
exfoliated WSe$_2$ monolayers affixed to single-mode optical fibers, we tune
the surrounding dielectric environment by encapsulating the flakes with
different materials, and perform polarized low-temperature magneto-absorption
studies to 65~T. The systematic increase of the exciton's size with dielectric
screening, and concurrent reduction in binding energy (also inferred from these
measurements), is quantitatively compared with leading theoretical models.
These results demonstrate how exciton properties can be tuned in future 2D
optoelectronic devices.
