Does anyone know if HaRav HaGaon Asher Weiss wears Techelet?
Also, why or why not?
He does not. (My Brother In Law learned in his Yeshiva).
He does not. He feels that archaeology cannot change a halacha and therefore we need not concern ourselves with the shaila. See Rabbi Aryeh Lebowitz here who address this: http://www.yutorah.org/sidebar/lecture.cfm/857737/rabbi-aryeh-lebowitz/ten-minute-halacha-why-do-so-many-gedolim-still-not-wear-techeiles-/