Question: How can I handle the financial stress better when I am paying more for bills than my boyfriend?
Answer: Is this an arrangement you agreed upon when you first moved in? Why are you paying more? Are you making more money? These are all questions, you should have explored before it came to this decision. As long as your boyfriend is contributing more in other areas, I think this is a fine arrangement as long as its temporary. If for example, your boyfriend makes less money than you or only works part time, you should both establish goals together, so that in the future you can split these responsibilities evenly. Otherwise, you will resent him down the line, and this might even break up your relationship.
Financial issues can be very stressful, especially if one person is carrying the heavier burden, but as long as you speak openly about these concerns, and figure out a new system that seems fair, you should make it through this experience stronger!