One of the advantages of running a Weber carb is that they are comparatively easy to re-jet. My DGV has easily accessible idle jets on the outside. Main jets and air correction jets are still in the float bowl, but It's easy to remove the top of the carb without disturbing the linkage (Try that with with a pair of Zenith WIPs).
To give an example of jet changes, Pat Braden's book on Weber carbs has a compensation table for "elevations" (altitude means you're flying) of up to 13,000 ft. Weber jets are measured in mm. (actually the equivalent airflow of an "ideal" jet of a measured size). Here are examples showing changes for main jets from the table:
0-5000 ft. 5000-6500 ft. 6600-9800 ft. 9800-13000 ft.
2.00 1.95/1.90 1.85 1.80 1.50 1.45 1.40 1.35 1.00 .97/.95 0.95/0.93 0.93/0.90
Note: the last line represents a percentage equivalent that might be applicable to other carb & jet combinations; often measured in thousanths of an inch. Since these jets meter fuel, a smaller jet means less fuel is provided at higher elevations to compensate for less oxygen density in the air. Less fuel also means less power (as Ole rightly points out).
I've spent the last few days dialing in my Weber, mostly by trial and error and starting with the suggested jet combinations in Braden's book. He shows how to troubleshoot, and correct flat spots and rough running at all power ranges. I've learned a lot about how to tune these carbs. Having the right jets combinations makes all the difference, and now I wonder why I suffered so long with an ill-tuned carb.
Good luck at higher "elevations", and try to keep your wheels on the ground. Leave the "altitude" to birds and aircraft.