How to control the order in which the markup for fields appears in the outputted html source for content? Is it possible to control (as in change) the order in which the fields appear in the html markup?

On admin page for a content type admin/structure/types/manage/&lt;content type&gt;/fields and in the Manage Fields tab, the fields can be dragged and re-ordered in the list.

However, looking at the outputted html source, the order does not change according to the order in this list. Is it supposed to? (I'd like to think it does).

I also looked at field_weight to control the order of the output but it unclear in what the author(s) of this module mean by 'weight'. Trying this module didn't appear to change the order in the resultant html source.
You can change tho order these fields are displayed from Manage Display (admin/structure/types/manage/CONTENT TYPE/display). Edit the weight there and the fields should be displayed in the selected order on the node view page.

Edit: In the fields screen (admin/structure/types/manage/CONTENT TYPE/fields) the weight is used for displaying the form fields in the edit/add content type form.