I have a question for you: Are their fears justified?
You see, the question is not really about size, it's more about the risks associated with size.
Have you honestly laid out all the risks that such companies might face by working with you and asked yourself how you have mitigated those risks? It's a better strategy than deflecting from the facts and hoping the company would take a gamble on you.
If you can lay out for them the risks that you know are true and genuine concerns and can show them how you have addressed those risks in your delivery model (If you have not done this, are you really prepared to handle such large accounts?) you will find that the question of size was never really the problem.