It doesn't sound like they've made you an enormous offer, otherwise you'd be writing this article from your new yacht, right?
Instead, they've made you a sensible offer. Are you at a sensible stage of your life? Do you have commitments and obligations that would suffer if you didn't act sensibly?
If not, don't be afraid to go yourself. Instead, take their interest as a vote for encouragement that your product has serious potential.
Try to raise capital instead of selling out. Offer them a cut as silent partners. Don't be scared if they don't agree initially. Practise your negotiation skills and see if you can't come to a mutually beneficial arrangement.
Perhaps they could take a cut of your business in exchange for funding, office space, access to HR, legal & Financial resources, etc...
The big change in these types of arrangements is that you will have to formalise your processes (read: boring, repetitive, bloated) and start sacrificing some of your product to suit the market. This is not such a bad thing in business and is necessary to allow growth, quality control and delegation.