Core strength enables you to keep weight on your spine and pedals instead of hands and saddle. Sometimes you can reduce hand pressure by lowering the handlebar because that forces your core to carry the weight of your upper body. A big gut can be an obstacle to going lower though. You can experiment moving your saddle backwards to see what effect it has. Moving the saddle back might create a more relaxed posture at the expense of reduced power which you might notice on long steep climbs.