In real life, we might expect a notched appearance from friction, as static friction might cause the piston to stick and then slip, stick and then slip. However, it doesn't look like this aspect is included in your model.
Instead, it looks like you're assuming that the nature of molecular collisions causes the pressure to increase a certain amount, at which point the (well-lubricated) piston moves to equalize the pressure, and then the pressure increases again, and so on. This isn't what happens; if the piston has a constant weight and the bore has a constant area, then the gas pressure is constant.
But—you might ask—the pressure arises from discrete collisions, doesn't it? Can't we magnify the line to show these? Yes, but it would still not look notched. It would vary around the constant-pressure line as a random walk whose amplitude deviations depend on the sampling time. With a sufficiently short sampling time, the concept of pressure loses meaning, as the momentum transfer from individual molecular interactions during that interval goes to zero.
A similar argument applies to the heating: There is no start–stop mechanism that would produce notches with a characteristic frequency. Heat transfer is a continuous process from the candle to various regions of the gas, again arising from random molecular collisions. It's not as if (as occurs in some computer simulations, sometimes problematically) the system iterates forward a step, for example, checks the total heat input, and adjusts the pressure or temperature in discrete increments.