Your "1000w" MW will want about 1500w input--read the info on the back label. You will want a 2000w inverter.
Meanwhile, that 1500w draw will be a 150amp draw on the batts. Two batts can't take that and hold up the voltage over 11v while the inverter is on, and the inverter shuts off if voltage goes under 11v (usually alarm goes off at 11 and it shuts off at 10.5 or so)
Which means you want four batts to supply that 2000w inverter to run your "1000w" MW
However! You can run a small MW like a " 700w" that actually wants 1000w input on that 1100w inverter and it might run for a couple minutes on two batts. Some MW jobs only take three minutes.
Another trick if you only have room for two batteries is to make those AGMs which can take the big MW draw without falling below 11v so fast. Now you can do it with two instead of four batts, at least for some shorter MW jobs.