I am applying for graduate school and one of the professors that I am considering to write my letter is an alumni from the school that I am to. Would this letter carry more weight?
If your professor did their graduate degree in the particular program you're applying to, this could help. The reason is that their letter can be more specific about the reasons you will succeed in that program: "She will be prepared to pass the quals in subjects X and Y immediately, based on her performance at Undergrad U., and will have no trouble passing the qual in Z at the end of the first year. Compared with the students who entered the Ph.D. program with me in 1992, she would have been in the top 25%." (This benefit can also apply when a recommender was previously on the faculty in the department you're applying to.) I do not think it matters so much whether current faculty remember your recommender personally. However, if the reputation or structure of the program has changed significantly since your recommender was there, their impression will be less relevant.
If your professor did only their undergraduate degree at this school, or a graduate degree in another department, then this will not matter or be noticed at all.