Cook beans in a large pot of boiling salted water until tender, 6–7 minutes. Drain, reserving 1 cup cooking water.
Transfer beans to a blender or food processor; add 6 Tbsp. oil, 1 Tbsp. lemon juice, 2 tsp. tahini, 1/4 tsp. garlic, and 1/2 cup cooking water. Puréee until smooth, scraping down sides of bowl and adding more water by tablespoonfuls if needed to blend. Season hummus to taste with salt, pepper, and more lemon juice, if desired.
Whisk remaining oil, lemon juice, tahini, garlic, shallot, and tarragon in a large bowl. Season to taste with salt and pepper. Add tomatoes and gently toss to evenly coat.
Divide hummus among plates. Top with tomatoes, stacking or layering slices. Drizzle tomatoes with juices remaining in bowl and garnish with tarragon leaves. Serve with warm pitas.