In a large bowl, combine graham cracker crumbs, melted butter, and sugar. Pour the mixture into the pan. Spread into an even layer, then press until the crumbs are compact. Refrigerate for at least 30 minutes. (The crust can be made ahead) Meanwhile, prepare the filling.

In a small bowl, soak gelatin sheets in cold water. Set aside.

Heat 1 cup of heavy cream, sugar, and salt in a small saucepan over low heat until small bubbles appear around edges. Remove from heat. Squeeze out excess water from softened gelatin and stir it into the mixture until gelatin dissolves. Set aside and let the mixture cool completely.

In a large bowl using a hand mixer or a stand mixer with the paddle attachment, blend cream cheese and cooled cream mixture until well combined.

Juice the blackberries by pressing them through a sieve in order to remove the seeds. Leave 1 tbsp of the juice in a separate small bowl (for swirl). Set aside. Pour the remaining blackberry juice into the cream cheese mixture.

Whip the remaining heavy cream (1 cup) with a hand mixer or a stand mixer with the whisk attachment until stiff peak.

Add lemon juice, vanilla extract, and whipped cream into the cream cheese mixture and beat until well combined. 

To make blackberry swirl, put 4-5 tbsp of the cream cheese mixture into a small bowl containing 1 tbsp blackberry juice. Mix until well combined. (optional)

Pour the cream cheese mixture into prepared crust and spread into an even layer. Spoon the blackberry swirl mixture in different spots on top of the cheesecake filling and gently swirl with a knife or toothpick. 

Cover with plastic wrap and refrigerate until the filling is firm for 6 hours or overnight.

To serve, remove the sides of springform pan and top with blackberries.