https://hc.weebly.com/hc/en-us/articles/201372693-How-to-Use-a-Domain-You-Purchased-Elsewhere

 On the Weebly Side:

Domain Options for Weebly Site 

You will wan to use “Use a Domain You Already Own”

IF YOU DO NOT CONFIGURE YOUR DOMAIN ON THEIR SIDE YOU WILL GET THEIR ERROR PAGE:

Do I need to change the nameservers for my domain?

No, Weebly does not support Nameservers for their hosting:

http://kb.weebly.com/nameservers.html

 DNS Settings:

DOMAIN	CONFIGURATION
TWO LEVELS (E.G. MYWEBSITE.COM)	point A-record (IP address) to 199.34.228.59
THREE OR MORE LEVELS (E.G. WWW.MYWEBSITE.COM OR BLOG.MYWEBSITE.COM)	point A-record (IP address)  to 199.34.228.59

 On the Dreamhost Side:

Go to your  Manage Domains Page  and make sure the domain is DNS only. If you have hosting on the domain, use the “remove” button under the “web hosting” column:

Once the domain is dns only, click the dns link under your domain name and add these records:

Custom DNS Options:

Name: subdomain, leave blank for naked/root domain

Type:  type of dns record, such as A record, Cname, TXT

Value: Target

Settings Needed for this setup:

Name:  leave blank for naked/root domain

Type:  A

Value: 199.34.228.59

---

Name: www

Type:   A

Value:  199.34.228.59

Note: This guide has been created to help simplify setting your domain up. The service you are pointing your domain to, DNS can/might has changed. Always check the hosts official page to verify the records.