Lets assume that the polarity is right, check with voltmeter. Inverted polarity is the most common cause for blown fuses in situations like these.
Are you sure that the batteries are 12V you should measure what the pole voltage is. Unloaded it should be around 12.8V. Charging a deep cycle battery with solar panel can take a really long time. It will take 60W solar panel around 25 hours to charge 100 Ah battery (that is even optimistic).
An inverter takes a lot more current than a cell phone charger even when the inverter is unloaded, the voltage of the battery will fall with load (and discharge) so to maintain the same power (Watts) the inverter needs to draw more current (amps) and that could be what is blowing the fuses.
Deep cycle batteries are intended for even slow discharge(for long time) were as car batteries have to handle burst of discharge when the engine is cranked. Boats are supposed to have separate electrical systems for engine and "consume". Our boat has 3 (4), 12V (std. battery) for engine and navigational lights , 12V (deep cycle battery) for "consume" usage like lights and radio , 24V (bank of deep cycle batteries) for winches and other power hungry equipment, that includes AC inverter when external AC power is not available.
Please let us know what was the cause.
Yours
Zweiblumen
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Sodomy non sapiens. : I'm buggered if I know
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