Jamie- Heritage is correct as B31.3 does referr back to ASME IX for qualifications. I noticed your Topic stated "B31.3 Procedure Qualification".
The weldment of the 4"/ 0.750 wall (Sch XXS?) weld-o-let to a 12 3/4 "/ 0.25 wall ( sch 20) pipe would not be a Procedure Qualification weld as tensile and bend test are necessary for a PQR testing which would not be available with these pipes welded to each other.
Note: When welding these pipes to each other the weld deposit only has to be a thick as the thinnest pipe wall--in this case 0.25" so the weld o let to pipe would not be a completely filled joint . This weld o let is very overkill for this weldment. I have seen this time and time again as weld o lets seem to be oversized for a lot of applications. Maybe because they only make them in certain sizes?
Refer back to your WPS for the range of thickness for this weld joint. If you don't have a WPS then you need to do the whole WPS/PQR test process to determine your range of thickness and diameters.
You did not mention the weld process nor any of the other variables.
More information given might get you gave a better question . If you don't know the questions to ask then maybe you need to make that known for more assistance and clarification as to what you actually need.
Ken K