If your stabilizer had one fuse, it would be simple to estimate the fuse rating. You say that the stabilizer is rated at 600 VA. Assuing that a single fuse is in the 220 V line: 600 VA / 220 V = 2.7 A. A manufacturer would probably round up to give some margin. But your unit has two fuses, so I don't know what this particular fuse is doing. Is it supposed to be subjected to the full load? If you just willy-nilly replace a fuse with one that is too large, instead of the fuse blowing, the equipment may be damaged -- some semiconductor may become a fuse -- much more expensive.
Since you have a 600 VA = 600 Watt stabilzer and a 250 Watt lamp, the unit is rated to handle the steady state load, but there is a the very large inrush current when the lamp is turned on. There will be ineffiencies from the step-down transformer etc. that raise the steady-state power consumption above 250 Watts, but it should even close to 600 Watts. Does the fuse blow at seemingly random times, or when you turn the enlarger on?
If the full current is flowing through the fuse, then it is operating close to its rating: 1.6 A x 220 V = 350 W. The lamp power (250 W) plus power loss in the step-down transformer may be approaching this figure. Then when you turn on the lamp, the current will be briefly higher. Is it a slow or fast blow fuse?
Frequently devices have written on them what fuse value to use.