Hesitation at 60 mph and up

OK, it is good to know that there are problems at idle. It will be easier to troubleshoot the problem at tilde than driving and if you fix the idle problems, it will probably fix the problems when running on the road.

Is this the original type of carburator?

At this point, you need to start doing some real tests rather than just driving the car and reporting symptoms.

A. Please check the fuel line under the car at all places back to the tank to make sure there are no leaks.

B. With the engine cold and off, remove the fuel line that feeds the carburator and place the line into a jar or can. Also, remove the center spark plug wire from the distributor for this test so that that car cannot start and run. Have someone crank the engine for 3 seconds and let us know how much fuel is pumped into the can. This is a simple test to see if the fuel pump and fuel supply is basically good for low speeds. Be careful to stay away from the fan belts and fan, etc.

C. I would suggest you try the test above listed by poisondart74, of taking off the air cleaner cover and putting your hand so that it covers a part of the carburator opening while the engine is idling and warmed up. This will decrease the air flow and also increase the gas flow. See if it does smooth out. Try to cover more and more of the carburator air opening to see what happens, and let us know.

D. Also look down into the carburator when it is warmed up and idling to see if:
1) the choke plate is fully open
2) there is not liquid gas being sucked donw into the carburator; lokk down into the carb throat with a flashlight for this check

And one test I did not mention above to see if the fuel sock is clogged: you can disconnect the fue line that feeds into the fuel pump and blow back into the tank with the fuel tank cap removed. You shoudl be able to blow back into the tank with some ease; if it is hard to blow, then the sock is likely to be clogged. (however, it is hard to tell if the feul sock is partly clogged this way.)

Do you have a vaccum guage for this testing? It could be very useful for this problem and does not cost too much.