Are there any micro-controllers which support writing data to large sized SATA disks?
SATA works at very high frequencies. If I look at this data connector sheet I basically see a TX/RX connection with differential signals because of the very high speed. 1.5Gbit of data would need to be proccesed, that's 1.5GHz signals. I've a feeling that it is a very high speed for a microcontroller to handle.
My best bet for you is to get a SATA to PATA converter and work with the PATA interface instead. It lowers the speed you need to look at bits, because the data is offered in a parallel way. That's still the easier way to work with.
I don't know whether you still want to use a microcontroller for that. I think a FPGA might become the better choice in such projects, but that depends on your goal.
Another option may be a high-end MCU with USB2 HS host, and use a USB-SATA adapter.
Think twice: You will also need a File System for large disks, and FAT32 has some design limits, esp. that Files must be < 4GB. Ohter file systems are much harder to implement on a µC. In most cases its easier to use a SD card, as it supports SPI.