A bit of search and you probably would find sources saying that perhaps it's around 6 x 10 to the power of 24, so a very big number. It's maybe more intriguing how this number was calculated, since gravity is what gives us the weight and with another field strength the result should be different!
That's why talking about mass seems more appropriate here, or also there's the option of assuming Earth's constants and using its diameter to calculate the weight.
However, this doesn't have a lot of value since everyone knows it would be more than any of the known quantities in the area, and a construction without real support, so a deception on its own.
What is really amazing tough is how some objects could have an incredible weight with a tiny diameter because they are extremely compressed. For instance the Sun is 100 times bigger (approximately) than this planet but its weight difference stays in the hundreds of thousands of difference. Other stars multiply this by an awesome factor!