Substituting Sugar with Caramel Syrup in Baked Cheesecake
Cheesecakes are oddly forgiving in my experience. I'd considering using 100 g to replace the sugar and see what happens. If you're worried about the added liquid and fat, I'd leave out roughly half an egg (meaning you'd need to beat it separately before adding half of it.) 

Having said that, my real recommendation would be to caramelize your own sugar. You can do so on the stove top and get it really dark if you're willing to crush it afterwards. (cook it in a pan until it's a nice mahogany color, then pour into a sheet pan lined with parchment or a silpat.) Or you can get lightly caramelized granulated sugar by placing it in a sheet tray in the oven at 300 degrees for several hours, stirring every 30 minutes, until it starts melting around the edges. At that point you'll need to stop. 

I sat that's my real recommendation because you can do a real 1:1 replacement with table sugar.