SMALL ACFT X MADE UNAUTH CLIMB TO OCCUPIED ALT. PLT DEVIATION.

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ACFT X WAS NOT UNDER RADAR CONTROL. THERE WAS TFC ACFT Y 1000' ABOVE HIM; AND TO THE SW. NON-RADAR RULES IN USE. PLT REQUESTED A CLIMB. WE ASKED HIM HIS POSITION FROM A VOR TO DETERMINE PROX OF HIGHER ACFT. PLT RESPONDED THAT HE WAS HAVING A VERY DIFFICULT TIME READING US; AND 'ASSUME THE CLIMB'S OK.' WE TOOK IMMEDIATE ACTION TO RECLEAR HIM TO ORIGINAL ALT AND ISSUED A NEW FREQ. ABOUT ONE MINUTE LATER WE OBSERVED HIS BEACON TARGET WITH MODE C INDICATING 4700'. I AM GREATLY CONCERNED WITH THE INCREASING FREQUENCY OF THIS TYPE OF PROBLEM WITH GENERAL AVIATION PLTS. WE SEEM TO BE SEEING IT MORE AND MORE; AND THIS YEAR'S TFC LEVELS WILL NO DOUBT BE AT AN ALL TIME HIGH. I BELIEVE THESE PLT'S NEED TO BE ALERTED OF THIS SERIOUS SAFETY ISSUE NOW; BEFORE THE HEAVIER TFC AND THUNDERSTORMS OF THE SUMMER SEASON ARRIVES! THE ACFT INVOLVED WERE A CONSIDERABLE DISTANCE AWAY FROM EACH OTHER WITH INCREASING SEPARATION. BUT WITHOUT ASCERTAINING THE PLT'S POSITION BEFORE WE ISSUED A CLIMB; WE COULD NOT BE ASSURED OF THEIR PROX. THE BOTTOM LINE IN THIS SITUATION IS THAT THE PLT HAVING A DIFFICULT TIME HEARING THE CENTER SHOULD HAVE STAYED AT PREVIOUSLY ASSIGNED ALT OR DECLARED AN EMER AND ADVISED US OF NATURE AND ACTION HE WAS TAKING. ASSUMING THAT THE CLIMB WAS OKAY WAS A DANGEROUS MISTAKE!