Assuming you have had this machine for awhile and it didn't used to do this under these same conditions, I'd say the problem is more likely in the drive train than in the carbs though it might also be be the engine. The easiest problem to find correct is the belt. Make sure it is within specs. I would look at the primary clutch next especially if you have not done regular maintenance (inspection and lubrication). The outer bushing (on the outside plate) will often wear out before it is noticed and can ruin the shaft it slides on. Corrosion on the shaft can increase the likelyhood of that happening. The weights on a machine that old did not have bushings and could easily be so worn that the weights don't swing in and arc perpendicular to the shafts they are mounted on. If the clutch has not been kept lubricated the weight rollers may be stuck, no longer round, etc which will obviously cause serious power loss. Compress the clutch with a bar or clamp (remove the belt first) to inspect the weights, rollers, etc. These are the most common and easily determined problems in the primary. The secondary could also be the problem and I think you will most likely find problems in that one to start with the sleeve bushing that rides on the part of the helix you see behind the mounted clutch. You should see light wear marks on the exposed portion of the helix but no serious scratching. If there are scratches or gouges in the helix it will need to be replaced along with the bushing. It could also be the slider buttons found internally though they rarely wear out.
The engine problem alluded to by a couple other posts would, I think, more likely cause starting trouble and/or fuel starvation at higher speeds due to fuel pumping problems. (That is the way to check it: spraying WD-40 or starting fluid by the seals.) Lack of decent compression (too much ring and/or cylinder wear) would more likely cause a lack of low rpm engine power.