What Rich Jones has written is technically correct but I think it needs a little explanation and context.
The "maximum" fillet size limit listed by Rich is only for LAP fillet welds, not for tee joint fillet arrangements such as the joint shown in the original post. The AWS D1.1 code includes this lap weld limit solely as an inspection aid. If the fillet weld on a lap joint is "full-sized", the top edge of the top lap plate is frequently subject to melting, therefore, making it difficult to verify (measure) the fillet weld size (either visually or with a fillet weld gauge). Note that the Code is not trying to establish the loading limits with this particular requirement. What was implied in the information by Rich Jones (and is explicit in the code) is that the fillet weld could be specified to be smaller than this based on the design conditions. The Code uses a restricted allowable stress for fillets (30% of the weld metal tensile strength). In other words, if the design loads were such that they were at the code limit of the base metal allowable stress, then a fillet weld would not be appropriate (a full penetration groove weld would be used instead). In fact, a single-sided fillet welded lap joint would not be possible under such a design case. For a tee-joint, a fillet weld might be possible, but it would become so large as to be normally impractical (again, a groove weld would be the appropriate choice).
Similarly, for ASME pressure vessels, they require a reduced joint efficiency factor of 55% for fillet welds (and also have a number of restrictions on where they can be used).
For pressure piping applications, a fillet-welded socket joint (normally used only for small diameter piping) would require the fillet weld leg length to be 1.25 times the pipe nominal thickness.
Therefore, for these "non-engineered" garage projects, the 2t weld face (or ~1.5 weld leg length) is probably an appropriate weld size selection. The original comment about weld sizes larger than this causing problems as well as being unecessary is an appropriate conclusion.
Tom Doody