How to install a new window header that overlaps an old one
Based on your description of the loading, I wouldn't be too concerned about supporting it at all unless you're going to leave the framing out for any significant period of time (days for example). If anything it might sag a fraction of an inch, but you'll true it up when the new header goes in.  You'll want to remove the old one first and re-frame that section of the wall, then cut in your new rough opening and put the new one in.  Pretty simple, and I've done this numerous times with patio doors.

If you're concerned about the weight, consider that there are quite a few houses out there dating from the time before building codes became common that don't have proper headers over windows and doors at all.  I've done several jobs where I had to install headers that were missing in the first place.  Also, I've done a couple garage demolitions where I had a hard time removing enough structure to make it collapse.