 Weldon won a scholarship (bursary) to the Bedford Modern School, which he attended until the age of 18, excelling in mathematics and the sciences before enrolling at King's College London to study Chemistry and Computer Science.He graduated with First Class honours in 1990, and was accepted to the Ph.D. program at Harvard University in Cambridge, Massachusetts, where he studied Physical Chemistry and performed research into the growth of diamond films on metallic surfaces with Cynthia Friend.He was awarded the Nottingham Prize for his thesis work.