As Duncan says, a primary balance weight introduces a secondary force at 90 degrees to the original, ( Hence the liking for 90 degree twins, fours, and V8s, where the secondaries from one cylinder balance out those from another cylinder. Although this introduces a horizontal rocking couple)
A three cylinder vertical is naturally out of balance, but a vertical six (Effectively two 3s back to back) is smother because one end of the engine balances the other, although not entirely free of couples.
The firing impulses will be asymmetric for a side by side two cylinder four stroke, as will the induction and exhaust pulses.
“Boxer” engines are smoother because the primary out of balance forces from one cylinder are balanced by those from the opposite cylinder. But as the number of cylinders increases, the greater the tendency for horizontal couples causing the engine to “squirm” about a vertical axis.
Steam locomotives, if balanced for horizontal forces (The reciprocating components) produced vertical force – hammer blow) which the civil engineers hated because of the damage done to the track.
One of the southern railway chief engineers avoided this, by not using balance weights, but gave passengers in the front carriages a very rough ride by jolting them back and forward, in time with the piston thrusts.
It is possible that the flywheel was drilled, deliberately to throw it off balance, to negate the out of balance forces from the balance weight on the crankshaft. (Some 3 cylinder engines have weights on the crank pulley and out of balance flywheels in an effort to produced better balance and smoother running). In which case the the parts must be fitted back in the original position. (Often by having an offset bolt hole, rather than a dowel).
Howard