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.
Just in case you’re new to the whole email marketing landscape, Aweber (along with MailChimp, ConvertKit, InfusionSoft, Ontraport and countless others) are email marketing systems designed to allow you to capture subscriber emails and then send them direct messages straight to their inbox. Some are very basic doing only email marketing, and some are full service systems that also include commerce and CRM capabilities.
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.