At the grocery store they were selling meyer lemons in mesh bags, they all seemed to be much softer than an ordinary lemon. Are meyer lemons supposed to be a very soft fruit? just touching them lightly was like I was squeezing a rubber ball, I can't even think of another fruit that would have that much give.
They should be quite a bit softer than a standard Eureka lemon, because the skin is much thinner. That said, it shouldn't be like a gentle squeeze causes your finger to sink in 1/2 an inch. If that happens, I think you've found a batch that are too old and have started to get mushy or lose moisture. Keep looking for good ones - Meyer lemons are terrifically fragrant, floral and mild.