No.
weighted DNS records are only available in MX records (for email servers)
there are sever methods of achieving the result your looking for though,
one way is with a router that will redirect a external IP address to a internal failover, Barracuda and Cisco have these kind of routers for example.
another way is using your own DNS servers. DNS servers can have a list of forwarders so basically you set up a DNS server that forwards it's requests to another DNS server that is ALSO your web server and it lists itself as the address for that A record. IF that server is off the first DNS server will use it's SECOND forwarder, which is ALSO a DNS server that lists itself as the A record for that address, etc....