Size really does matter from a customer's perspective. I have faced and sold through objections like "what if you run out of money" and "how do we know that you'll be able to scale if we deploy across the whole organization." These are all things that if they are unaddressed, can kill a deal.

With customer success stories with large companies, you are incredibly well-armed to address these concerns.

Here are just a few things smaller companies can do better:

More responsive and personalized customer service and support.
Demonstrate a willingness to listen and move fast to incorporate feedback and new features.
Fix things faster.

If you garner praise from your customers via social media and email, ask them to repost it along with a picture and their first name in a well-designed "praise" area of your site.

In terms of getting through objections raised by a potential customer, your sales team should be encouraged to do anything possible including contractual language in the SLA or a side agreement. These should always be done with consultation of legal counsel but the point is that there are many ways to satisfy a company of the concerns of dealing with a vendor is who is "small but growing"

Happy to talk more about this in a call.