While the exact value of the electron's mass was determined through a series of experiments and refinements, it's generally attributed to Robert Millikan for his groundbreaking oil-drop experiment in 1909.

Here's why:

* Millikan's oil-drop experiment allowed him to measure the charge of an electron with remarkable precision.

* Knowing the charge of an electron, scientists could then combine this with the known value of the electron's charge-to-mass ratio (determined by J.J. Thomson earlier), to calculate the electron's mass.

Therefore, while Millikan didn't directly "weigh" an electron, his work was crucial in establishing the electron's mass with a high degree of accuracy.