No, you don't have to pay again. If you made yourself a bootable USB flash drive installer for Mountain Lion then use it to install Mountain Lion on your MBP. If you don't have one then be sure the MBP has Snow Leopard or Lion installed. Go to the App Store and sign in with the same Apple ID used to purchase Mountain Lion. Click on the Purchases icon in the toolbar, locate the listing of your Mountain Lion purchase. Click on the Install/Download button to the right of the entry.
Now you may wish to read the following related to making a bootable USB flash drive installer:
Make Your Own Mountain/Lion Installer
1. After downloading Mountain/Lion you must first save the Install Mac OS X Mountain/
Lion application. After Mountain/Lion downloads DO NOT click on the Install button.
Go to your Applications folder and make a copy of the Mountain/Lion installer. Move
the copy into your Downloads folder. Now you can click on the Install button. You
must do this because the installer deletes itself automatically when it finishes
2. Get a USB flash drive that is at least 8 GBs. Prep this flash drive as follows:
a. Open Disk Utility in your Utilities folder.
b. After DU loads select your flash drive (this is the entry with the mfgr.'s ID and size) from the left
side list. Click on the Partition tab in the DU main window.
c. Under the Volume Scheme heading set the number of partitions from the drop down menu to one.
Set the format type to Mac OS Extended (Journaled.) Click on the Options button, set the
partition scheme to GUID then click on the OK button. Click on the Partition button and wait until
the process has completed.
d. Select the volume you just created (this is the sub-entry under the drive entry) from the left side
list. Click on the Erase tab in the DU main window.
e. Set the format type to Mac OS Extended (Journaled.) Click on the Options button, check the
button for Zero Data and click on OK to return to the Erase window.
f. Click on the Erase button. The format process can take up to an hour depending upon the flash
3. Locate the saved Mountain/Lion installer in your Downloads folder. CTRL- or RIGHT-click on the installer and select Show Package Contents from the contextual menu. Double-click on the Contents folder to open it. Double-click on the SharedSupport folder. In this folder you will see a disc image named InstallESD.dmg.
4. Plug in your freshly prepared USB flash drive. You are going to clone the content of the InstallESD.dmg disc image to the flash drive as follows:
a. Double-click on the InstallESD.dmg file to mount it on your Desktop.
b. Open Disk Utility.
c. Select the USB flash drive from the left side list.
d. Click on the Restore tab in the DU main window.
e. Select the USB flash drive volume from the left side list and drag it to the Destination entry field.
f. Drag the mounted disc icon from the Desktop into the Source entry field.
g. Double-check you got it right, then click on the Restore button.
When the clone is completed you have a fully bootable installer that you can use without having to re-download Mountain/Lion.
Note: The term Mountain/Lion used above means Lion or Mountain Lion.
As an alternative to the above (you still have to do your own download of Lion/Mountain Lion) you can try using Lion DiskMaker 2.0 that automates the process of Steps 2 through 4.