Did Eddington's 1919 eclipse photographs really prove Einstein right?

Mostly yes, but the answer is a more interesting story than "photographs proved Einstein right". The evidence from 1919 was thin, partly cloud-spoiled and argued over for decades, and the verdict held up anyway.

The test: the Sun bends starlight, and general relativity predicts 1.75 arcseconds at the Sun's edge, twice the Newtonian value. During the total eclipse of 29 May 1919, two expeditions photographed stars near the darkened Sun and compared them with positions measured months earlier. One team went to Príncipe, off West Africa, with Eddington; another went to Sobral in Brazil. Eddington was a Quaker who had declared himself a conscientious objector in 1918, and it was the Astronomer Royal, Dyson, who proposed that he undertake the expedition.

The data were messy. At Príncipe a storm hit that morning; Eddington, busy changing plates, barely saw the eclipse, and cloud interfered with the star images. In his notebook he wrote that one plate gave a result agreeing with Einstein. At Sobral the main telescope's blurred images were discarded, though its estimates were closer to the Newtonian prediction, while a smaller backup telescope gave the clearest images, slightly above Einstein's prediction.

Was the analysis biased? From 1973, doubts surfaced that Eddington's team skewed the results, a worry popularised in The Golem by Pinch and Collins. But a modern reanalysis suggests his analysis was accurate and less afflicted by bias than some later ones, and a 1979 remeasurement of the Sobral plates supports his results.

The final word came decades later: only radio-astronomical measurements in the late 1960s definitively showed the full predicted deflection.