How do you make a large grafitti stencil?
I have never done one, but for a large stencil, I would probably use a program like the free Paint software which comes with windows.  

Start by changing your image size to enormous proportions calculated by multiplying your desired stencil size in inches by the dot-per-inch resolution of your printer.  

In the software, zoom out until you can see the whole image space and then draw some light colored lines both across the page from edge to edge and from top to bottom.  The resulting grid is going to help you align the printed pages with each other later in the process.  

Now paste in your desired image and stretch it to fit the image size.

...then choose the print menu option.  On the option screen, turn off the "stretch to fit page" checkbox, then click the print button.

The program is going to do is subdivide your "too-big-for-a-page" graphic into a matrix of pages, each containing a portion of your image.  

Cut off the unprinted borders and then line up the light colored lines until every page is in its' place.  Then tape them all together.

Next it is time to grab an exacto knife and remove the stencil parts where you want the paint to get through.  This is where the fine cut details are going get troublesome.  You might be able to glue (or tape) toothpicks (or thin wire) to the front of such details to strengthen them up a little.

When your stencil is completed, turn it over and spray the back with a repositionable spray glue.  Make sure that all the details get enough glue on them to hold them onto the target surface without curling.  Once the glue is sticky, you can apply the stencil to the target surface, rub down all the edges and get to painting.

The spray glue will make up for the flimsiness of your stencil material and as long as you apply your paint lightly, the printer paper should suffice to keep the shielded areas paint free.

You may need to trace your applied stencil with your xacto knife after the paint dies, just to assure clean edges and unwanted peeling.