Never added a 1/2" to a 1/4" blade tang. I have added some 3/8" tang extensions.
First, don't weld, braze. Namely silver braze, though there's no reason regular bronze brazing won't work. Silver brazing doesn't cause grain growth like welding does. you weld it and don't do a couple-three normalizing cycles you going to end up with sugar sized grain in the joint that will cause it break very very easily. It can be done and has been done, but it's way more trouble than it's worth. Much simpler and easier to silver braze. Not to mention you can silver braze with a Mapp gas torch and a bit of silver brazing wire and some borax for flux.
Best way I've found is to grind about 1/2" or so of the end of the tang to a tapered wedge, and cut and grind/file a notch in the extension you'll be using. The joint should be fairly tight, but not air tight like a guard fitting. Heat it up, protect the guard and blade from heat with a wet rag, add a little flux on the rising heat and braze together. You want it just hot enough to flow the silver braze, not over heat the steel. Hard to explain, not real hard to do. After brazing let it cool down slowly and do a couple heats to a dull red in the joint and let air cool. You'll bend the steel and break it before the silver braze lets go if you did it rite. This is if it's a non air harding steel like 1084 or even 5160 or 52100(though they will air harden somewhat), not some of the higher alloy stainless, though it should work with them, just haven't tried it and figured out how to spot temper the joint.
While not quite as easy as sticking an arc welder to it, much safer for the blade integrity and longevity.
I've done it with a mapp gas torch, but it's a lot easier with a fine pencil tip on an oxy/propane or oxy/acetylene rig. Just make sure to keep the blade and guard cool during the cool down and brazing.