Weak spark, retarded ignition timing, and a lean mixture can all give those symptoms. Since the engine is fairly simple, it usually make sense to pull the carb apart, yank the flywheel off, and pull the head, i.e. check everything.
With the carb, the fuel seat can fall out (very common). Nothing holds it in but a tight fit. Also the main jet-adjuster tends to get full for crud. Just remove it with a 7/16" wrench and eye-ball it. Jiggle the float and make sure it's empty aslo.
Tecumseh (R.E. Pehlon) aftermarket condensors are often crap. So, it's imperitive to check the condensor (for short, for capacitance, and for holding a charge). Make sure no wires were left hanging out and got cut by the flwheel (also common). After setting the point gap, check when timing is taking place and adjust the stator plate if needed.
You mentioned the possbility of a valve sticking. Yes, it's possible and also very easy to check. Sticking exhaust valves are more common with Kohlers, burnt ex-valves more common in Tecumsehs, and loose exhaust seats in Briggs. Just pop the head off and look at the valve face - and check how tight it is. Taking a head off and on is a ten minute job and a new head gasket is rarely needed.
When we used to take in these things for repair, diagnosis of one particular problem was rarely worth the bother. That mainly because the engines are so simple, you can pull apart and check all the systems pretty quick.
A sticking exhaust valve will not sound the same as when an engine has weak spark, late spark, and/or a lean mixture - but the difference can be a subtle one.