Simple to reproduce.. this is done on SharePoint 2013 Foundation on a "Team Site".
1) Go into Site Pages and add a new "wiki page"
2) Change the Page Text Layout to "Two Columns with One Header"
3) In the Header insert "Search box" web part.
4) In the left column insert a search "Refinement" web part.
5) In the right column insert a "Search Results" web part.
6) Save the page and go back into "non-edit" mode.
7) Now we simple want to make the left column 25% of the width and the right column 75% of the width. So click on the Page menu (next to the Browse), drop down the Edit box and select "Edit in SharePoint Designer".
8) the designer will open up and show the code. At the bottom you will see 2 rows with the text: style=width:49.95%; ...... Change the first instance to 24.95% and the second instance to 74.95%
9) Exit Designer and choose to Save the page (don't reload it).
10) You should find yourself back the original SharePoint Page in the Browser.. press the [F5] key to refresh and everything disappears!
Followup...It appears as if you alter the width right after step #2 (right when you create the page but before you add any web parts), you can then add your web parts afterwards. However it's scary to think that if I wanted to adjust the width again later I can't without having to completely rebuild the page with all my custom refiners