Not so much the weight but the actual force needed to pull it (Force meter will work for any force!). Put some potatoes or a paint can in the seat to represent y our electrics. Rolling friction will be a significant factor as will the friction is the gearbox etc. I repeat - it is essential to be able to disconnect the mechanics from the 'pusher'. The sad fact is that enough effort to produce effective charging over a significant time will make the pusher very annoyed - particularly if they are near home and can charge it as soon as they get in the door.
You should take some time to measure
absolutely everything you can think of associated with this project. At some stage you will find that things are not going to plan an that information will help you to think your way out. All the retired engineers on this forum will be nodding their heads at this point! (And even the young ones)
Yep. Your experimental pushes will tell you the power and the torque needed (Force times wheel radius). Then you will need to decide on a motor AND the appropriate gearing / transmission. It will have to be something that is off the shelf. Perhaps a toothed belt from motor to the axle with two appropriate pulleys. You can try various combinations of pulleys easier than using an actual gearbox (despite it probably being more efficient)
Which brings up the question of whether you can realistically use the same (brush) motor as a generator. An alternator is much more efficient - particularly at low at low turning speeds. Look at what's used in small wind generators - always alternators. So you would also need to couple to the generator. Sharing the same belt may not give the optimum charging as driving.
PS This may not be what you want to hear but electric wheel chair users get on fine with a beefy battery pack and charge it at home. I have a friend who has a range of four or five miles from one charge and chair plus user are much heavier than a stroller plus kid. In the conclusion to your final write up, that option could be mentioned if you want Engineering Credibility.
You could also Google Electric Powered Stroller. Loads of ideas there.