Is your content just a piece of code that for now you placed in a text widget, or is it an actual widget from a plugin?
When you say you want to embed it in all post and pages do you know where? Weaver II has many HTML insertion areas that you can use to add something to all posts and pages depending where you want it. But weaver II is now really old and I don’t fully remember all of them. If you go to Advanced options > HTML Insertion, you will find them and you ca test them by adding some text in them and seeing where it ends up.
As you know you should update to Xtreme and it also has HTML insertion areas that could be used for this.
Edit: If your content is an actual plugin widget, there is a plugin called widget shortcode that allows you to insert a widget inside any content area using a shortcode