My husband is worried that if I put too many rocks in there, it will be stressful on the tank. As long as the edges of the stone aren't in contact with the glass surface on the bottom of the tank, do I have anything to be worried about?
The two main concerns would be rocks touching the glass or the structure collapsing and "touching the glass" LOL. Keep in mind that when you add 100lbs of rocks to the tank you're not increasing the weight by 100lbs, but 100lbs - the weight of the water that they take up (~8lbs/gallon IIRC). So yes the tank weight ends up heavier, but not as significantly as you may first think.
Another thing to consider though is that if you have a 60 gallon tank, but you fill it up 1/2 way with rocks, you've only got about 30 gallons of water. The process of waste --> ammonia --> nitrite --> nitrate, in the end relies on the nitrate levels being diluted by your water volume. If there's less water overall relative to your stocking rate, you may need to do water changes more often.
As far as rocks displacing water volume, this doesn't really apply to the stocking rate from an aggression standpoint, as the rockwork helps break the tank into more territories and can help reduce aggression if done correctly.