As you probably are aware, The Weekly Poet is currently closed to unsolicited submissions. However, Chapbooks for Charity, a site run by the same person as The Weekly Poet, is taking submissions for its upcoming collaborative chapbook on mental illness.
In addition, Muscle & Blood, a print literary journal that shares an editor in common with The Weekly Poet, is taking submissions that relate to issues of socioeconomic class.
I hope this is helpful to you, and expect to see The Weekly Poet open for submissions again in a couple of weeks.