"he claims that our overseas manufacturing is not welding our parts well enough so he wants to increase the weld sizes on everything we design"
I went through this very same thing years ago with Chinese suppliers. Their weld beads were slightly larger than what we had done on our in-house welding, but the welds broke at the interface, i.e., they "pulled out" of the base metal. Obviously their weld procedure was flawed, but our management wouldn't attempt to force correction. They were too in love with the low prices and the butt-kissing, pandering salesmanship they got from the Chinese reps. The company president's solution was to have them put larger weld beads. Of course, they held more force before they broke, but they still broke the same way. Neither I nor any of the welders or supervisors would come forth and spell it out for them because we suspected that we would all lose our jobs to "outsourced manufacturing". Such poor manufacturing practice should have immediately disqualified them as unfit, unknowledgeable amateurs, but it didn't.
So duk748, the supervisor's solution may or may not work. It depends on where the overseas manufacturer is not welding "well enough" and why that is not "well enough". On the leg of the fillet to the 80x80x6 tube, anything over 6mm is theoretically wasted welding. You are limited by the 6mm wall thickness' strength, so welding a bead further out along that wall doesn't gain anything. It just shifts the leading edge of the HAZ, and gives a larger HAZ, which is generally not what you want. I could see going halfway up the 20mm edge of the plate, i.e., 10 mm, with that leg of the fillet to "make it look right", but the governing factor is the weld throat depth. Using 75% of 6mm might be the proper theoretical design, and might be all you really need, but a 4.5mm fillet sure wouldn't look right with a 20mm plate edge next to it, plus to make sure you get all the way around the tube's corner the bead will likely need to be larger than 4.5mm.
A 6x10 fillet might be hard to do and would actually end up ~7.5x10, but that's the limit of what I would do (assuming no out of the ordinary loads). That tubing is going to melt much quicker by the weld arc than the 20mm edge of the plate so the arc needs to start against the plate edge and spend more time over it. The supervisor's solution of a 15-20mm weld is definitely overkill against that 6mm tube wall. A lot of people with a little exposure to general welding have seen those big, thicker-than-the-base-metal fillets done in multi-pass welding on big structural pieces but don't understand the reason behind it. "Bigger is better", right?
So what is going to happen here is that the supervisor will get his way with the 15-20mm welds, which will likely be strong enough to hold, so he'll say "see, I told you so" thinking he solved the problem. Of course, this merrily neglects the doubled or tripled welding time. Then eventually the overseas manufacturer will try to raise the price, or skimp and cut back somewhere else, like on material quality.