It looks like you may have a configuration issue. According to the weebly site it looks like you only have to worry about the A records.
http://kb.weebly.com/domain-registrar.html
You should turn off the Web Forward. That is more than likely your issue. You can test this by running a TraceRoute from a command line to your site c:\tracert websitename.weebly.com You will probably see it sometimes get forwarded to the site and sometimes get directed to 199.34.228.100.
You should do either a Forward or an A record change. According to the link I put there it appears Weebly only wants you to change the A record then assign the domain in their Site Editor
I have had friends who have had this same issue in the states. I normally direct them to a great domain registrar I use called Fast Web Builder. http://fastwebbuilder.com
Their domain manager and hosting control panel are one in the same so it really takes a lot of guess work out of managing your domain names and websites. They even have hosting located in Sydney so it may work out better for this part of the world:
http://fastwebbuilder.com/au-hosting/
They even have VPS, Semi Dedicated and fully dedicated servers so when your site grows you don't have to learn all new software.
http://fastwebbuilder.com/au-vps-hosting/
So to recap, the reason this is the issue is once you configure weebly to know a domain name is pointing to it, the subdomain, for all purposes, goes away. So right now either you did not configure the weebly side correctly or it's all your DNS. It could be working because half of the time the Domain is Forwarded to the weebly subdomain or it's A record.
I hope this clears everything up for you. Good luck with your site!