Folau, who is an Evangelical Christian, created a firestorm of controversy in Australia, and in rugby circles, after he wrote on his Instagram page that gays would be condemned to "hell" if they failed to "repent".
His comments were described as "very disappointing" by Qantas airlines, a major sponsor of Rugby Australia, while international referee Nigel Owens, who came out as gay in 2007, said such comments could contribute to young people taking their own lives.
Weber, who played his only test for the All Blacks in 2015 and is likely to be in contention for selection again this year, said he was disappointed that players had stayed silent.
"Kinda sick of us players staying quiet on some of this stuff," the Waikato Chiefs' Weber wrote on Twitter. "I can't stand that I have to play this game that I love with people, like Folau, who say what he's saying.
"My cousin and her partner, and my Aunty and her partner are some of the most kind, caring & loving people I have ever had the pleasure of knowing.
"To think that I play against someone that says they'll go to Hell for being gay disgusts me."
Weber's stance has drawn praise in his homeland with a New Zealand Herald column labelling him a "modern-day rugby hero", while rugby columnist Paul Cully wrote on Fairfax Media's Stuff website it was Weber's "...biggest tackle, bringing down Israel Folau" over the comments.
The New Zealand Rugby Players' Association also backed Weber's stance.
"Obviously it's personal and he felt strongly about it," NZRPA chief executive Rob Nichol told Stuff.
"His message is 'I don't like that negative stuff from Israel, I don't respect it, and I'm going to send a positive message in this space'. Good on him for doing it."
New Zealand Rugby, which was recognised locally last year for its diversity and inclusivity policies, also used social media to tacitly support Weber.
"New Zealand Rugby is committed to Diversity and Inclusion, and welcomes people from all walks of life," NZR said in a post on its Instagram page.
"We respect that people have different views and beliefs, however expect that any opinions and views are expressed in a respectful way."
(Reporting by Greg Stutchbury; Editing by Peter Rutherford/John O'Brien)
