Rabbi Weiss is definitely Orthodox. He is not Hasidic or Haredi, and perhaps he is controversial with that segment of Orthodoxy. He has begun a Yeshiva called Chovevei Torah.
http://www.yctorah.org/
" Openness and Ideology of halakha
What exactly does the YCT slogan, "The Open Orthodox Rabbinical School" mean? In a statement prepared exclusively for The Commentator, Rabbis Avi Weiss, Dov Weiss, and Dov Linzer explained: "Our Yeshiva is firmly implanted in the Modern Orthodox community. It is a modern Orthodox Yeshiva. Because of the move towards insularization in the Orthodox community we have been using the adjective "open" to describe our commitments. We are fervently Orthodox with an unwavering commitment to Torah and halakha. At the same time we are intellectually open and we strive for greater inclusiveness in practice.
"Intellectual openness means that we encourage questioning and critical thinking as essential components of one's full avodat Hashem. In the context of Talmud Torah, this includes the integration of "outside" disciplines, such as academic Talmud, history, legal theory, and philosophy.
"Openness in practice means a willingness to interact with all Jews and to seek out within Halakha greater inclusiveness for women and non-Observant Jews."
Hmmm. Sounds pretty Left to me.