A B737-700 ON A CIRCLING APCH TO JAX WAS SLOW TO GET LINED UP AND STABILIZED; GETTING A 'SINK RATE' GPWS AT ONE POINT. THEY CONTINUED AND LANDED.

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WE WERE INBOUND TO JAX WITH RWY 7 ADVERTISED ON THE ATIS. CAPT ASKED FOR RWY 13 TO CUT DOWN ON TAXI TIME. I ASKED APCH CTLR FOR RWY 13 AND HE SAID TO EXPECT IT. WE BRIEFED AN ILS TO VISUAL RWY 13. CHKED ON WITH ENSUING APCH CTLR AND HE ASKED IF WE'D LIKE ILS RWY 7 CIRCLE TO RWY 13 TO SAVE SOME TIME. CAPT SAID YES AND WE SWITCHED OVER TO THAT PLAN WITH A QUICK BRIEF (WE WERE EXPECTING A VISUAL APCH) OF THE APCH TO RWY 7 WITHOUT A LOT OF DISCUSSION REGARDING THE CIRCLE OR THE CLOSE PROX OF THE 2 RWYS THRESHOLDS. WE BROKE OUT OF THE OVCST AND HAD ARPT IN SIGHT AT APPROX 1800 FT MSL. THE CAPT CONTINUED STRAIGHT AHEAD TOWARDS RWY 7 FOR 200-300 FT BEFORE I ASKED HIM IF HE WAS STILL PLANNING ON CIRCLING TO WHICH HE REPLIED YES. HE THEN DID WIDEN OUT TO THE L; BUT NOT FAR ENOUGH TO BE ALIGNED WITH RWY 13 BY 500 FT. I FAILED TO TELL HIM THAT WE SHOULD GO AROUND AND HE FAILED TO GO AROUND. THE GPWS ALSO GAVE US ONE 'SINK RATE' WARNING AT APPROX 300 FT AGL (WITH NO 'PULL UP' WARNING) WHICH ALSO SHOULD HAVE CAUSED US TO GO AROUND. WE CONTINUED AND LANDED RWY 13; BOTH REALIZING THAT IT WAS A LESS THAN IDEAL APCH. IN THIS CASE; FOR THE AMOUNT OF TAXI TIME WE WERE GOING TO SAVE; WE SHOULD HAVE GONE AHEAD WITH THE ADVERTISED RWY 7 APCH. WHEN WE BRIEFED RWY 13 WE SHOULD HAVE PROBABLY STUCK WITH IT RATHER THAN SWITCHING BACK TO RWY 7 WITH A CIRCLING APCH. WHEN WE SWITCHED BACK TO RWY 7 WE SHOULD HAVE JUST DONE A STRAIGHT-IN APCH SINCE THE LAST MIN ASPECT CAUSED US TO MAKE SOME ERRORS WITH THE CIRCLE. AS PLT MONITORING I DEFINITELY WILL STEP UP MY LEVEL OF ASSERTIVENESS IN QUESTIONING THE CAPT WHEN I SEE SOMETHING THAT HE OR SHE IS MISSING. MY EXPERIENCE LEVEL WITH CIRCLING APCHS IS LIMITED AND WHILE I THOUGHT WE NEEDED TO MAKE SOME CHANGES I ALLOWED MYSELF TO FALL VICTIM TO THE THOUGHT THAT 'THE CAPT MUST KNOW WHAT HE IS DOING -- HE HAS MORE EXPERIENCE; ETC.