I have 2 rounded square borders (of 2 different colors), and one innermost rounded square from a svg, as shown here http://i.imgur.com/TjFQTfu.png. I would like to enlarge the innermost while keeping the WIDTH/THICKNESS of the 2 outer borders. How do I do that using Inkscape?

If that image is made with each square being the same shaped path but with a different stroke width given, then if the scale strokes with the objects icon at the top is disabled (as already) , you can scale them just as anything else.
If you want to scale the paths without changing the radius at the corner's curves, then use the node editor tool.

I tried to resize while F2 doesnt seem to work. http://i.imgur.com/K95dDrU.png

This is what it looks like separately: http://i.imgur.com/txwZfsx.png

I am editing a svg so I'm not sure how it was made.

Here is an example how it would work like a charm:


The node editor tool is not even necessary for that, have to correct the previous post.

Yea this is what I get:


The borders increased, even though you saw that I did not enable those 4 affect options.

If I am doing it wrong please ELI5

Download the previous example svg and open it in inkscape to see how it would work.

It needs your original svg redrawn, but nothing complicated.

Sorry this is actually my first time working with svg (had to edit someone's file) and using inkscape (or illustrator for that matter), all I know what you did was you made 3 rounded squares of different sizes, centered them with different colors, and finally group them into 1 object. I did the same thing, but it is still the same. What am I missing?

Actually those were made without rounded corners, each having only 4 nodes, with only their stroke width differing.
Those rounded corners are made by rounded joins above eachother, and, the was not toggled.
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Attributes-Stroke.html#Attributes-Stroke-Join