I would just like to mention that in addition to the many shared research interests of Siegel and Weil, they were clearly well acquainted with one another, with both attending Max Dehn's seminar on the history of mathematics over a period of years. From pages 124-127 of Yandell's book "The Honors Class" and pages 51-53 of Weil's "The Apprenticeship of a Mathematician", it shows that Siegel attended the seminar regularly from 1921-1935 while Weil began attending in 1926 and during subsequent visits to Frankfurt says "as often as I could". So Weil's high esteem for Siegel is doubtless influenced by personal interaction at the seminar (and elsewhere) in addition to familiarity with his research.