Boosting algorithms: Confusion between "weak classifiers" versus "number of boosting rounds"
I went back to the original paper from the literature by Schapire (http://www.cs.utah.edu/~piyush/teaching/brief_intro_boosting.pdf) and it does sound like a weak classifier is the output of a boosting round. Consider how the output of the overall classifier is $$H(x)= \text{sign}\left(\sum_{t=1}^T\alpha_th_t(x)\right)$$ which is expressing a threshold for the sum of $T$ weak classifiers.