According to Watts: The main focus of my research has been to use geological and geophysical techniques to study the Earth's crust and upper mantle beneath the world's ocean basins and their margins.

A major part of my research has been to quantitatively understand the phenomena of flexure, how it depends on load and plate age, and how it contributes to the gravity and geoid, the crustal structure and, the stratigraphic patterns that develop in sedimentary basins.

His science is distinguished by the application of the principles and methods of geophysics to the solution of major geological problems.

These include isostasy, lithospheric flexure, the origin of deep-sea trenches and mountains, sedimentary basin formation, the deep structure of continental margins, oceanic islands seamounts and mid-ocean ridges and the relative roles of plate processes such as flexure and mantle dynamics in contributing to Earth’s gravity and topography field.

He was the 2015 Harold Jeffreys Lecturer of the Royal Astronomical Society[12] and in 2020 the recipient of the US Navy and American Geophysical Union Maurice Ewing Medal.