Your ignoring that you have 70ish Kg of body weight there already
exactly, if you put 70kg on one pedal then you've 3 options, either;
1) tip the bike over so that that pedal is verticaly over the wheels (and either align your COG with it too, or apply a torque to the handlebars)
2) apply force to the bars to ballance it, the wider the bars the less force needed
3) fall off
As the pedal push and bar pull are not on the same axis either laterally or far more imprtnatly along the length of the bike your assumptions amount to gross errors really and your maths becomes bunkum.
Looking at the bike form the side makes no difference, you cant weelie/endo without really trying (and invoking some momentum) therefore there is no pivot. Looking at it from the front or back the pivot is the tyre contact patch. You've either got to ballance the push/pull of the pedals with a small push/pull on the wider bars or lean the bike as you pedal so that the lever disapears and the force on the pedal acts directly down on the pivot point. The difference in height of the two forces results in a moment on the bike (for the sake or argument the pivot is the riders COG) and the reaction force is the latteral grip from the tyres.