All of the Weebly themes include space for a logo at the top of the site.
To change the logo on your site:
Log into your Weebly account
Click the Build tab at the top of the page
Scroll over your site name text at the top to see your options, as shown below
You can turn this off, write a text title for your site, or (drrummrooll!!!) upload a logo.
Click the Logo option
When prompted, select a logo from computer or through an image URL
You can upload a JPEG, GIF, or PNG file. For your logo to look it's best, it should be less than 150 pixels tall and in PNG format. PNGs use a transparent background, so you don't see a white box surrounding your logo image.
Tip! If you don't have a logo image, and probably won't have one designed anytime soon, but want to have a stylized look for your site we'd recommend sticking with just a text title instead of a logo image. Use one of the Decorative fonts for your text title, which are found found in the Design tab, via the Change Fonts option.