the plastic box is the "wobbly", but if you have assembled it, it's been fairly stable. then "wabbelt" only when the cover on and make.
For us it is under a small canopy and therefore well protected against rain. I think if they would stand in the pouring rain were the pillows not 100% sure.
Frazit:
OK for the money, but nothing earth shattering. if you need some stabilization is turned on and quality higher quality want, you should grab a little deeper into their pockets.