Weeks' research contributions have mainly been in the field of 3-manifolds and physical cosmology. He is particularly interested in using topology to understand the spatial universe. He has created a computer program SnapPea to study hyperbolic 3-manifolds.
Weeks is also a noted author. His book, The Shape of Space, explores the geometry and topology of low-dimensional manifolds. The second edition explains some of his work in applying the material to cosmology. He has also developed interactive software to introduce these ideas to middle-school, high-school, and college students.