The custom domain name feature allows you to setup your Weebly site with a domain name you've already registered through Namesilo. The changes we request are simple, but Namesilo has been nice enough to make this even easier by adding one-click integration with Weebly to their DNS Management page.
As they note on their own support pages:
To apply a DNS template simply navigate to the Manage DNS page for your domain and then scroll to the bottom of the page where you will find a section for "DNS Templates". You can apply the applicable template by choosing Weebly and then clicking the "Apply Template" button on the right-side of the page.
After you do this, a popup window will appear showing you the DNS record changes that will be made. We will display the records that will be added as well as any records that will be deleted. The changes that are displayed are the changes required for your integration to succeed. Simply click the "Accept" button in the popup window and your DNS template will be applied.
Visit their DNS Manager help here:
Once you've made the changes, be sure to assign the domain name to your site. You do this vis Settings > Change Site Address within our editor.
Note that it can take your registrar up to 48 hours to update their servers with a change like this one. It usually doesn't take more than a couple of hours, but this is something to keep in mind. Nothing is happening on our end when you point a domain here (it's either pointed here correctly and it works, or it is pointed here incorrectly and it doesn't), so we can't speed the process up.