Guinea pigs are grazing animals so it's normal for them to spend most of their day eating. But the majority of what they're eating should be hay.
I think giving her floor time rather than an exercise cage would be better. For my piggies I give them a section of the room and place hay on different areas (it encourages some exploration). Like someone before me said that can also be done with veggies
I would also agree with getting her a friend. One of mine used to be lazy too until he saw how curious his cage mate was about everything. Now they both spend a lot of time exploring and running around!
My last tip would be to get lots of toys, hideys, and TUNNELS! Piggies loooove running through tunnels. I have a pretty long tunnel that they just run in back and forth several times. The longer the tunnel, the better

they also like jumping between hidey holes, and toys would give them the curiosity they need to explore
I'm sure your sow is fine. You can check her heft by feeling around the rib cage.. If you can feel her rib bones then she should be fine, but if you can't, then she could be overweight!
Anyways best of luck to you
