AIRSPD AND ALT OVERSHOOT NEAR HOUSTON; TX.

Narrative

CLRED TO 4000 FT AFTER TKOF WITH TSTMS IN THE AREA. I WAS DISTRACTED LOOKING AT THE RADAR DEPICTION AND DID NOT HEAR THE 1000 FT PRIOR TO LEVELOFF WARNING. THE HIGH-SPD WARNING WENT OFF AT 250 KIAS; SO I PITCHED UP TO SLOW THE ACFT. THE DEP CTLR EITHER CAUGHT MY CLB PAST 4000 FT OR COINCIDENTALLY ASSIGNED 5000 FT AND I LEVELED THE ACFT AT 5000 FT. MY PERCEPTION OF THE PROB WAS INACCURATE. I MADE A POST ANALYSIS AFTER THE HIGH SPD WARNING AND CLBED INSTEAD OF REDUCING PWR. I DID NOT THINK WE HAD CLBED TO NEARLY 4000 FT AND TOOK THE WRONG ACTION TO SLOW THE AIRPLANE. I BELIEVE THE WX WAS A DISTR AND FATIGUE PLAYED A PART. SUPPLEMENTAL INFO FROM ACN 495762: MY CAPT WAS CLBING OUT OF 3000 FT. WE WERE CLRED TO 4000 FT. ALL OF A SUDDEN OUR SPD WENT THROUGH 250 KTS AND CONTINUED UP TO 275 KTS. I WAS WATCHING HIM TRY AND SLOW DOWN AND AS A RESULT WE WENT THROUGH 5000 FT; 1000 FT PAST OUR ASSIGNED ALT. ATC THEN TOLD US TO MAINTAIN 5000 FT. DETERMINING FACTORS: 4TH DAY OF A 4 DAY TRIP; LATE NIGHT FOLLOWED BY A LONG DAY; BAD WX ATC DELAYS AND CAPT'S LACK OF TIME IN THE AIRPLANE AS WELL AS FLYING WITH THE AUTOPLT INSTEAD OF HAND-FLYING TO RECTIFY THE SIT.