The issue is that Eclipse wants Java 7 ('Version 1.7'), but OS X demands that you have Java 6 ('Version 1.6') installed in order to use Java applications. So, Eclipse starts, sees Java 6, then quits and tells you to upgrade to Java 7. If you use Java 7, OS X won't let you start Eclipse.
The fix is to install Java 7 (which you already have), uninstall Java 6, then symlink Java 7 to where OS X expects to find Java 6.
As per this link, the procedure goes like this:
# Remove Java 6
sudo rm -rf /System/Library/Java/JavaVirtualMachines/
sudo rm /private/var/db/receipts/com.apple.pkg.JavaForMacOSX*
sudo rm /usr/bin/java
sudo rm /Library/Java/Home
# Symlink Java 7
sudo ln -s /Library/Java/JavaVirtualMachines/jdk1.7.0_65.jdk /System/Library/Java/JavaVirtualMachines/1.6.0.jdk
sudo ln -s /Library/Java/JavaVirtualMachines/jdk1.7.0_65.jdk/Contents/Home/bin/java /usr/bin/java
sudo ln -s /Library/Java/JavaVirtualMachines/jdk1.7.0_65.jdk/Contents/Home /Library/Java/Home
(I'm not at my Mac to try this, but I had to do this to get Eclipse to work myself)