RBeckett has some great advice.
I do a lot of stuff with 0.063" wall square tubing (actually, I think almost all of my welding projects have used it). I have a Millermatic 211, which should be pretty similar in capability to your machine. The first thing to remember is that that tubing is _VERY_ easy to burn through. The second is, sheet metal likes to buckle. Use LOTS of tack welds. Tack it every 2 inches at least. The other thing is, if you don't need to weld out fully, don't (IE, if you don't need a liquid tight seal, don't weld the whole seam). Another technique to consider is something called "backstep" welding (well, at least that is what Jodi on WeldingTipsAndTricks.com calls it). Check out some of his videos to see the technique. You also don't want to weld large stratches at a time, the heat is going to cause issues. So do short sections (say, 1") at a time. Oh, I tend to use 0.030 wire IIRC.
The main thing about welding thick to thin is where you direct your heat (as others have said). This more or less amounts to pointing the gun more at the heavy side, and less at the thin side. I like to at the weld joint, almost directly at the thick part, and let the weld puddle grow and envelop the thinner side. I have tried the "swirl" method RBeckett describes, but think I need more practice. In any case, practice on some scrap and get your voltage and wire feed rate tuned in before you start on the real parts. In general, I run at about the same feed rate for the thicker material, but at slightly lower voltage, but it's a balancing act.