still feel like too much of my weight is supported by my hands
May need to stretch out some, sounds like you are cramped up a bit. That can affect breathing and comfort quite a bit, like wearing a coat that's too small. You want a stem long enough to allow you to pull on the bars when seated climbing and sprinting.
I push my seats all the way back on the rails, and use long stems. Stock stems are always way too short for me, so I generally get something longer. I tell people to try to stretch out horizontally as much as you can, but keep your main body mass directly over the bottom bracket, centered between the wheels, for the best comfort on long rides.
People's instinct is to sit upright with all their weight on the back tire, and when that doesn't work, they get a softer seat and a taller stem. Never works.