Answer: Currently we only allow domains to connect to free sites if the domain is registered through Weebly. If you are on a grandfathered account we allow the external domain to remain connected as long as the site address is not changed. Sorry again for the inconvenience. Please let us know if you have questions about our current plans. Source: https://community.weebly.com/t5/Domains/No-More-Custom-Domain-Name-For-Free-Accounts/td-p/94518
Of course, you could dispense with a custom domain name altogether if you had to, saving yourself $120/yr. Since Weebly still lets you use a whatever.weebly.com type name for free, you would still let everyone view your website but without the appeal of that custom website name. Or as a compromise, you could simply buy the whatever.com domain name and simply redirect it (ie point it) back to your free Weebly whatever.weebly.com site (saving $90/yr).
Nevertheless, it was an unexpected hit that surprised myself and some of my unsuspecting clients. Just one more thing to consider. However, onward and upward.