Weir Farm National Historic Site Amendment Act - Amends the Weir Farm National Historic Site Establishment Act of 1990 to: (1) require visitor and administrative facilities for the Weir Farm National Historic Site in Connecticut to be located in Fairfield County, Connecticut; (2) keep development of any property acquired for such facilities to a minimum; (3) permit the acquisition of previously developed property without remediating such development; and (4) require development agreements with local governments having jurisdiction over any property acquired.