Weight and force of jumping person The other day my daughter was standing on my back. She weighs, let's say, 35 kg. I assume that the force involved is product of gravity (as in $F=ma$)?
Then, she jumped off my back, and suddenly the force increased significantly (and painfully). Am I correct in assuming that the mass involved didn't change, in which case, it had to be the acceleration? If so, what happened? How did she change the acceleration caused by gravity, and by how much?
 A: You are correct, her mass did not change. And while gravity is still acting on her, what she did was use her legs muscles to store energy (like springs) such that the resulting spring force was greater than the force caused by her mass (weight).
So if you look at the force balance you get:
$$\text{Leg Force} - \text{Weight} = \text{mass} \cdot \text{acceleration}$$
Where $\text{Weight} = \text{mass} \cdot a_{\text{gravity}} $
So when $\text{Leg Force} > \text{Weight}$ you get a net positive acceleration in the direction opposite gravity (up) which causes her to "jump" off your back.
A: Let's think about this in slow motion:
When your daughter was standing on your back, the constant force you felt on your back was solely due to gravity (only her weight).
But, the moment she started pushing you down to jump upwards, you began to feel an additional force which has nothing to do with gravity but Newton's Second and Third Laws of Motion. 
These laws simply state that, if you are gaining speed in some direction, you must be pushing something else with the same force in the opposite direction. This is the Third Law of Motion and this wass the force (in addition to the force due to your daughter's weight) that gave you that pain. 
And how much the force will be (hurt) depends on how much speed your daughter gained in how little time. In other words, how much your daughters acceleration was. And this is the Second Law of Motion which is expressed by the famous equation F=ma.
A: Before jumping, your daughter's weight was balanced by the Normal Reaction force exerted by your back on her feet. 
Then your daughter used her leg muscles to store energy in it. At the moment she jumped, that energy was released. This energy was used to push against your back (which was the cause of that pain), and since force exist in pair, there was a reaction force exerted by your back on her. 
As she was in equilibrium earlier, an additional force made her go up. 
Hence the force that she applied on your back, and which also caused the pain, and the force that made her jump are part of action-reaction pair. 
