It just took a couple of weeks, but Tapbots has added support for 3D Touch to the Tweetbot 4 app (currently US$4.99).
There's full peek and pop support in the timeline. "Touching" a tweet brings it forward for quick viewing of details like the number of favorites and retweets, while the same action on a Twitter avatar brings up details about the account:
Perhaps the nicest new feature is the quick action menu from the Home screen. With a press, a quick action menu appears showing choices for Tweet, Tweet Last Photo, and Show Activity. The update is free for all current Tweetbot 4 users. If you haven't yet purchased the app, be sure to buy it before the price goes up to $9.99 soon.