How to bridge a gap between two countertops?
The easiest way to do this is buy a piece of 1x3 lumber.   Cut a piece to go across the back and screw to wall (predrill your lumber).   Put a piece in each side and screw to cabinets.   You do not have to make your sides the full length - you can hide the ledgers and make the counter look floating.   

If you know your counter material you can deduct that to get the height of the boards you are drilling in so your counter matches flush on both sides.  After your ledgers are done you can glue or screw the counter down or even use finishing nails depending on counter material.   b

This is a very non-invasive method that will cost you $5-6 in lumber and 6 screws plus a little wood glue.   This will look better and won't sag and will assure that counter meets up well with existing tops.