Unable to alter SPI speed on Arduino Micro
As was pointed out in the question comments, your use of unsigned int is the problem. The prototype for SPISettings is:

SPISettings(uint32_t clock, uint8_t bitOrder, uint8_t dataMode) {


The comments in spi.h say:

// We find the fastest clock that is less than or equal to the
// given clock rate. The clock divider that results in clock_setting
// is 2 ^^ (clock_div + 1). If nothing is slow enough, we'll use the
// slowest (128 == 2 ^^ 7, so clock_div = 6).


So your SPI speed will be the processor speed divided by 128, which is 16 MHz divided by 128, being 125000 Hz, which is your observed result (since unsigned int cannot possibly hold more than 65535 on this platform).