One thing I have learned when paper piecing is the pressing ... can sometimes stretch the thread and it will look like the tension was too loose and resulting in the seam thread showing. It typically happens when joining two "units' together and there is the most bulk. This can also happen when removing the papers. Avoid stressing/stretching the seam/thread. Use the smallest stitch to get the most perforations in the paper, and check your needle size. Different fabrics will react differently in paper priecing, so do make a small sample withthe thread and the thicknesses and the needle. Sometimes I find the smallest needle works the best ( this is counter intuative). If you are pressing each piece as you go and if you use steam the steam and or starch the mosture will allow the thread to stretch through all of the thickenesses. There is one more method, and that is to remove the papers in the units prior to joining and pinning the junctions/match points.
As for making adjustments now ... you could try to re- stitch exacty over your existing stitch line.... but this is probably not the option you are looking for.
I have done the fine marker thing myself.
I am anxious to see the other solutions that get posted.