Don't understand your application. Plug weld over tube with 1/16" wall thickness? Maybe you want to post this on "Welding, Bonding & Fasterner Engineering" forum.
when calculating weld size, it depends on stick/parent material used, throat size and expected loading.
Last time i designed a weld i used "design of weldments handbook" to give me an allowable stress per mm/2. Then manipulated as required to determine leg length.
We use 5/64" metalcore for flat welds. I had about 10 years or so welding experiance in one of my past lives.
My hip-shot response would be "as small as the welding operator can make it and still maintain proper profile, penetration and not have excessive porosity".
Beyond that, when we get into a tricky situation, we run some test welds, bend them and send out for x-rays.
