My interpretation of your answer: ASME Section 1 A-250.2.3 Thickness t. t is the thickness of the weld, of the pressure–retaining material, or of the thinner of the sections being joined, whichever is least. If a full penetration weld includes a fillet weld, the thickness of the
fillet weld throat shall be included in t. This definition is convoluted and is misleading because of the term 'weld'. To make it simple and clear, t is the thickness of the thinner section at the weld. This applies to both butt or fillet weld. I'm happy if ASME accepts such plain language and willing to correct this!
Just for the benefit of any other reader of this discussion, I'm listing below other 'related' code definitions of similar situation - inspection acceptance criteria.
Page 76 of ASME B31.3 Table 341.3.2 : For groove welds, height is the lesser of the measurements made from the surfaces of the adjacent components; both reinforcement and internal protrusion are permitted in a weld. For fillet welds, height is measured from the theoretical
throat, Fig. 328.5.2A; internal protrusion does not apply.
ASME Sec VIII Div 1 page 150 UW-51: t the thickness of the weld excluding any allowable reinforcement. For a butt weld joining two members
having different thicknesses at the weld, t is the thinner of these two thicknesses. If a full penetration weld includes a fillet weld, the thickness of the throat of the fillet shall be included in t.
ASME Section IX QW 191.2.3: t is the thickness of the weld excluding any allowable reinforcement. For a butt weld joining two members having different thicknesses at the weld, t is the thinner of these two thicknesses. If a full penetration weld includes a fillet weld, the thickness of the throat of the fillet shall be included in t.
ASME Sec I A -250.2.3 Page 205: t is the thickness of the weld, of the pressure–retaining material, or of the thinner
of the sections being joined, whichever is least. If a full penetration weld includes a fillet weld, the thickness of the
fillet weld throat shall be included in t.
ASME Sec V Fig T-434.2.1 page 47 Notes (h)
Weld thickness, t, is the nominal material thickness for welds without reinforcement or, for welds with reinforcement, the nominal material
thickness plus the estimated weld reinforcement not to exceed the maximum permitted by the referencing Code Section. When two or more
base material thicknesses are involved, the calibration block thickness, T, shall be determined by the average thickness of the weld; alternatively, a calibration block based on the greater base material thickness may be used provided the reference reflector size is based upon the average weld thickness.