PRIVATE PLT TAKES OFF IN MARGINAL VFR CONDITIONS AND FLIES INTO IMC.

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WX WAS MARGINAL VFR MOST OF THE MORNING. WX WAS OBSERVED TO BE +6 MI AND 2100 FT CEILINGS 10 MI N OF OUR DEPARTING ARPT (GYY). WX BRIEFLY IMPROVED AND WE DEPARTED TO THE N. I EXPECTED VISIBILITY AND CEILING TO CONTINUALLY IMPROVE. THEY REMAINED THE SAME FOR 15 MI THEN RAPIDLY REDUCED TO IMC. UPON ENTERING IMC I PERFORMED A 180 DEG TURN TO RETURN TO VFR CONDITIONS; VISIBILITY CONTINUED TO REDUCE. CONTACTED MIDWAY FOR VECTORS OUT OF IMC. THEY VECTORED US TO MIDWAY INTXN (PGM 2100) WE CONTINUED SINCE WE WERE NOW VFR WITH FLT FOLLOWING. CONTACTED CHICAGO APCH FOR CONTINUED FOLLOWING. WHILE ON THEIR VECTORS WE BUSTED DUPAGE (DPA) AIRSPACE. WAS INSTRUCTED BY CHICAGO TO MAINTAIN HDG. WHILE ON HDG WE BUSTED DUPAGE'S (DPA) CLASS D AIRSPACE; ALT 1500 FT. IMMEDIATELY CONTACTED APCH; REQUESTED FREQ CHANGE; CONTACTED DUPAGE TWR; INFORMED TWR OF WHAT HAPPENED. HE APPROVED THE OVERFLT OF THE ARPT AND ENTRY INTO CLASS D. CONTACTED APCH AND CONTINUED ON COURSE. HOW THIS COULD HAVE BEEN PREVENTED: WHEN VISIBILITY DID NOT IMMEDIATELY IMPROVE; I SHOULD HAVE TURNED BACK TO GYY. WHILE ON VFR FLT FOLLOWING I SHOULD HAVE PAID BETTER ATTN TO WHERE I WAS AND CONTACTED DUPAGE SOONER (OUTSIDE OF HIS AIRSPACE). CONTRIBUTING FACTORS: TOO MUCH FOCUS ON TRYING TO GET TO DEST ON TIME. (WE HAD ALREADY BEEN DELAYED FOR A DAY AND A HALF.) AND AFTER EXITING IMC; I WAS FLUSTERED AND NERVOUS FROM THE ORDEAL. PUT TOO MUCH FAITH IN CTLRS TO KEEP ME LEGAL. I SHOULD HAVE REMAINED MORE VIGILANT AFTER MIDWAY.