How can I insist people register to enter my weebly site?

Which app, tool do you suggest?

If you require a registration to your Weebly website before they can access your form or any page, you can enable the membership in Weebly:

https://www.weebly.com/blog/membership-is-here

https://hc.weebly.com/hc/en-us/articles/203859426-Membership-User-Registration 

https://hc.weebly.com/hc/en-us/articles/203859386-Membership-Limiting-Page-Visibility-to-Members