It makes perfect sense that a 13mm belt is, in general, more expensive than a 10mm one. Besides the actual difference in price, we also have to take into consideration other aspects.
Although a 13mm belt is great for certain exercises, it should come as no surprise that the number of these is not that great. Most athletes prefer this type of belt for exercises like squats and other compound movements, but for some individuals, it can be really uncomfortable in certain situations, like getting into the starting position for deadlifts.
The lack of versatility of the 13mm belt can cause some problems and it may force you to have a second belt for other exercises, which means another spending.
One solution to those problems could be to have a 13mm belt for the exercises that do not create any issues, and a second comfortable Velcro belt for the rest of the exercises that do not require top-level support. The Velcro belts are decent in terms of support, and their price is fairly small.