If you count the weight of the servers required to service all the funds at the institutions his money resides at, and the percentage of his funds compared to the overall amount at that institution, it still might be tons.
but what if you only accounted for the drives in the servers that contained the data ? would it still hit that 'multiple ton' threshold
Literally has literally been destroyed:
"Used for emphasis while not being literally true." [1]
If his keeps his money in $100 bills, then you're right. $136 billion would weigh about 1,230 metric tons.
More likely, his cash consists of electronic entries in bank systems which weigh substantially less.