Welcome @KendraStewart to the Instructure Community!
I did some testing and it looks like what will work is to create an additional assignment group for the additional project and give it a 15% weight. If you include that weight within the 100% total for the class, then that weight will be ignored for students who are not able to complete the assignment in that group. Their final score will be based on the weighted amount out of 85%. So a non-honors student who got a perfect score on all the homework and exams would have an overall score of 100% because their weighted scores add up to 85%/85%. For those students who do get assigned the additional project, their total possible weighted amount would be 100% instead of 85%. So an honors student who got a perfect score on all the homework and exams but did not complete the additional project would have an overall score of 85% because their weighted scores add up to 85%/100%.
Another option is to keep your current weight settings for homework and exams and make the additional assignment group worth an additional 15% weight. The additional project would then become extra credit, with the possibility that an honors student who does well on the homework, exams, and the additional project could end up with an overall score of 115% because their weighted scores add up to 115%/100%.
I’m going to mark my response as a solution, but there can be more than one. I hope our colleagues here in the Community share other options.