If you have a custom domain name example.com that you purchased from Weebly, you have a couple of options.
You can leave the domain with Weebly and through domain name management section of your account you can edit the DNS records to point the A records to the IP addresses of your new Magento host.
Alternatively, you can migrate the DNS management by pointing to different nameservers to manage the DNS records elsewhere like Cloudflare or Amazon Route 53. This is a help article on that: https://hc.weebly.com/hc/en-us/articles/201184656-Manage-Nameserver-Records
Finally, you can transfer the domain to a different domain name registrar like GoDaddy, NameCheap etc. This would then be where you renew the domain each year. To do this you will need to unlock the domain https://hc.weebly.com/hc/en-us/articles/216733938-Unlock-Your-Domain-and-Get-the-EPP-Code
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