Reading the Weimar constitution and at Art. 109 it states men and women are equal before the law (which I'm assuming includes the constitution):
Article 109: All Germans are equal before the law. Men and women have the same fundamental civil rights and duties. Public legal privileges or disadvantages of birth or of rank are abolished. Titles of nobility shall be regarded merely as part of the name and may no longer be bestowed. Titles may only be bestowed when they indicate an office or profession; academic degrees are not affected hereby. Orders and decorations shall not be conferred by the state. No German shall accept titles or orders from a foreign government…
Which can be interpreted as allowing a woman to be elected president however reading Art. 41 and Art. 46 suggests otherwise:
Article 41: The Reich President is elected by the whole German people. Every German who has completed his thirty-fifth year is eligible for election…
Article 109: The Reich President appoints and dismisses officials of the Reich and officers as long as no other provisions are adopted by law. He can allow the right of appointment and dismissal to be exercised by other offices.
I am however aware of using a default "he" meaning "they" in older texts and other languages.
So could a woman have been president? Were there any prominent candidates?
Yes, a woman could have been elected president. However, neither the Social Democrats nor the Communists, who had advocated for women's rights to vote and to be elected, ever had a female candidate. Those were the most likely parties to have female candidates at all. Despite their agenda, even in these parties, women were not promoted or much supported, in fact they were delegated to work groups and to fields that were seen as typically womens fields.
The only notable woman that held a high position in parliament, but not the state, was Klara Zetkin (Communist Party) as Alterspräsident (Old Age President).