The installation instructions for MPLAB X are rather sparse. They only say “it requires 32-bit compatibility libraries”. Assuming you already have Java installed (which I did, because I had installed Eclipse before). Prior to wheezy, all you need to do was install ia32-libs. Now, after the upgrade to “multiarch” you should:
dpkg --add-architecture i386 apt-get update apt-get install ia32-libs-i386
Now you can install MPLAB X.
Update: Microchip’s blog says you can do it like this. I haven’t tried, so YMMV.