A recent 42-day experiment on ISS, where mice were allowed to reproduce in weightlessness and produce offspring, has found that the weightlessness environment not only causes significant harm to mice conceived and born under these conditions, it appears to carry that harm down to at least the next generation.

From the abstract, which labels the first generation offspring as F1 and the next generation F2:

In the NASA Rodent Research 20 mission, we examined the impact of a 42-d spaceflight on the female reproductive axis including ovulatory capacity, implantation rate, and fecundity as well as behavioral, metabolic, and functional outcomes in F1 and F2 offspring. Females bred 5 d after return to Earth became pregnant but only exhibited a slight decline in fecundity compared to ground controls.

In contrast, F1 offspring from spaceflight dams exhibited marked growth, functional, and behavioral differences compared to F1 offspring from control dams. Moreover, F1 female offspring from spaceflight dams exhibited decreased ovarian reserves as evidenced by reduced anti-Mullerian hormone levels early in life (21 d of age) and premature ovarian failure or an early loss in fertility, as indicated by reduced numbers of litters and total number of pups born to females over a 9-mo period.

Strikingly, transgenerational metabolic and reproductive disturbances were also observed in F2 pups of spaceflight granddams, including persistent reductions in ovarian reserve, suggesting germline-level effects.

In other words, mice babies conceived and born in space exhibited serious issues that were also carried over into the next generation.

Though a number of similar studies have been done previously on ISS, the research is generally limited and inconclusive. Experiments on Earth duplicating lower or zero gravity suggest it has no effect on reproduction. This study however tested actual weightlessness, and found it decidedly harmful for newborn mice and later generations.

The results strongly argue that no woman should allow herself to become pregnant while in space. This conclusion might change given time, but I have my doubts. This result is what most people assume about the consequences of conception in weightlessness.

It also argues strongly for the need of some form of artificial gravity on future long term interplanetary space vessels. Without it, space travel will be significantly limited.