In the world I am building there are rat-like primates called iolasae, or mane-beast, which are the new world equivalent of great apes. In this family of primates there are sentient humanoid creatures called lokk, They have digitigrade legs, long arms, short legs and prehensile tails. I would like for them to have two prehensile tails. Is it possible and if it is how much weight could these tails support?
...the animal probably won't be very big.
While not a prehensile tail, an elephant's trunk is capable of lifting 300kg and it contains no bones whatever. Note that an elephant's trunk is attached to an absolutely enormous animal of around 4535kg for a lifting capacity of 6% of body weight. On the smaller end of the scale, a spider monkey is completely capable of holding itself up by it's tail alone. Note that this follows the trend of smaller creatures lifting many times their body weight, such as ants lifting 100x their body weight.
An animal could be designed to have large powerful prehensile tail(s) but it would need to be designed that way and supported by an interesting evolutionary history (if your story needs that kind of evidence). I'm not sure of an examples of an Earth animal with two tails so that will be a very interesting evolutionary history. There are many instances of Siamese twins that have convergent or divergent spinal columns. Having two tails is definitely possible, it's just a matter of making them that way.