I had this same problem a few years ago and if I'm remembering correctly (by no means a guarantee
) The Auxilliary Water Pump is fed from the same fuse as the A/C Clutch. If your Aux. Water Pump is seized (as many are) or taking too much load, then it will blow the fuse when the compressor clutch tries to engage. Try disconnecting the Aux. Water Pump (there is an inline connector about 9" from the pump) and see if that solves the problem.
I'd agree with 'okyoureabeast', don't use a higher rated fuse as you risk burning out the wiring.