Mike DeHaan began writing professionally in 2010 as the sole proprietor of DeHaan Services.To see this information with the best background image, please refer to "About.Me", befriend me at Facebook, or circle me at Google+.
Weebly's "Blog Author" widget from the Blog Sidebar's Elements menu provides a lot of flexibility. You can change both the title and the text.
It has all the capabilities for text editing that you find in most Weebly text widgets.
At this point, I don't see a way to code any HTML in this widget.
The "Picture" does what you expect: it displays an image of your choice. I just added my home-made picture of "Copyright DeHaan Services 2013" as the top element in this sidebar on Jan. 22, 2013.
The "Search Box" is a "Pro" feature; if you're paying for Weebly hosting, it may be worthwhile.
The other widgets are pre-programmed to do what they say.