Grease the sides of the pan.
Beat cream cheese for 3 minutes until creamy. Add sugar and beat for 2 more minutes, scraping the bowl as needed.
Mix in sour cream. Add eggs one at a time, mixing until combined. Add vanilla and salt with the last egg.
Pour one-third of the batter into the crust. Spoon one-third of the blackberry sauce on top and gently swirl.
Repeat layers, finishing with a swirl of sauce on top.
Wrap the bottom of the pan with foil and place in a larger roasting pan. Add hot water to create a water bath.
Bake at 325°F for 60-75 minutes until slightly jiggly in the center. Turn off the oven and let the cheesecake sit for 1 hour.
Remove from the oven and cool completely. Refrigerate for at least 6 hours before serving.