By using an ESP (like Aweber, Mailchimp, etc) means that you are sharing part of your "reputation" with thousands (or even millions) other senders. So even thou most of the ESP are quite efficient in cleaning-up their customer base from spammers, the more clients they have, the more it's difficult.
Here you can find an pretty accurate and updated analysis of ESP's clients "quality": http://mainsleaze.spambouncer.org/may-2017-in-spamtraps-esps... Aweber is #6, which is not a good signal.
That said, you may switch ESP by choosing one that provides a you custom "identity" such as dedicated IP, DKIM, PTR, SPF records (which usually means quite a lot of setup and costs) or choose an ESP that doesn't have tons and tons of clients, eventually with a free version.
http://www.emailvendorselection.com/ is an updated ESP directory. You are of course also welcomed to try mine: http://www.mailup.com