What electoral system did the Weimar Republic actually use?
Proportional representation w/ no thresholds IIRC
That's correct. Pure PR. No thresholds or direct seats. At least in Reichstag elections.
President: Popular election. If no candidate received more than 50%, a run-off was held with a simple plurality of votes being sufficient now.
Interestingly, candidates could be replaced between the two rounds. As a result, the candidates in the run-off weren't always the same candidates which had stood in the first round. In addition, all candidates from the first round could theoretically participate in the run-off too. So, no candidates were actually eliminated with the first round (except for those who chose to drop out or who where replaced by their respective parties).
Example - 1925 presidential election
First round
Karl Jarres (DVP, also endorsed by DNVP): 38.8%
Otto Braun (SPD): 29.0%
Wilhelm Marx (Zentrum): 14.5%
Ernst Thälmann (KPD): 7.0%
Willy Hellpach (DDP): 5.8%
Heinrich Held (BVP): 3.7%
Erich Ludendorff (NSDAP): 1.1%
Second round
Paul von Hindenburg (endorsed by DVP, DNVP, BVP and NSDAP): 48.3%
Wilhelm Marx (Zentrum, also endorsed by SPD and DDP): 45.3%
Ernst Thälmann (KPD): 6.4%