Yeah, you need to setup either canonicals or a custom robots.txt for this. Unfortunately that's not super easy in Weebly.
I believe some of their templates have a "header code" section that you can edit. If you have that for each blog post (NOT the overall site settings) then just add your canonical to each one. The canonical should be the main blog post permalink. This will tell Google that all the other versions aren't the ones you want to "count."
I'd have to find a client with a Weebly to login & check it myself but I do believe you can edit these page by page. Let me know if you want me to take a deeper look.