Instead of simply sending out a broadcast sporadically, why not choose to create a newsletter. That way, you can send one out each week/month that includes said promotions, offers, site updates, etc. in one place. That way, subscribers won’t get annoyed of you sending out too much content to them, as they can expect to get everything in your regular newsletter.
With your one person in mind, create an editorial calendar around those conversations and challenges they’re having. Try to work with one theme at a time, so that you can pull 3 or 4 of your posts into an ebook or slideshare later on. Writing in themes also helps brand your content because you can create a journey for your readers (almost like a free course).
One of the best features of AWeber is the ability to create a series of emails that are automatically sent out to new subscribers. This allows you to create an eCourse or some sort of introductory guide for your latest subscribers. This is fantastic as you can market it as an incentive for people to subscribe (e.g. subscribe and get our free 7 day eCourse) and once setup, you can leave it to be sent out automatically.
Now, you can automatically send highly relevant emails encouraging them to buy the product or service they were considering. Customers who received multiple abandoned shopping cart emails are 2.4 times more likely to complete the purchase than those who receive only one followup email, according to Experian. Try sending the first message one day after, a second message 48 hours after, and possibly a third message within three or four days of abandonment.