Uppose you have configured a health check for four weighted records each with the same weight (25). What happens if one of them goes down?

Route 53 will not route any traffic to that server. That is, Route 53 will not respond with the IP address of any server that is down. Suppose that the web1-east instance goes down out of web2-east, web1-west and web2-west. Its weighted record has a weight of 25, but as soon as the health check fails, Route 53 effectively changes this to 0. It does not actually change the value of the weight to 0 in the record, but for all practical purposes, it becomes 0. That leaves 3 weights each 25, which add up to 75. Web2-east would get 50% of the traffic, while web1 and web2-west would get about 50% of the traffic.