Is covariate significant in logistic regression Im going to investigate if a disease have a negative impact on the development of children. The disease is the independent variable with additionally confounders. 
Tests from the study have shown that birth weight is significant different between the control group and group with the disease. If I do a logistic regression with the disease and birth weight as independent variables, I get birth weight as a significant variable. My question is that if birth weight differs between the groups, can that affect or be the reason that it is significant for the outcome? Can some bias have occurred?
 A: This is an old question but remains unanswered so I will give my own two cents.
From your post, I understand your main question is about if the presence of a disease causes some developmental change in children.  I've used that word, "cause", deliberately.  If this is the case, here is a simple DAG which might explain your research design.

Here, $x \to y$  is the direct effect of the disease $x$ on the outcome $y$.  The effect is confounded since birth weight $w$ offers a backdoor to $y$ through $x \leftarrow w \to y $.  Conditioning on $w$ closes this backdoor, but does that mean that the estimated odds ratio of $w$.
Here, I've also included $U$, unmeasured confounders of the effect of birthweight and the outcome, if they exist.  Let's suppose they do exist for a moment, because it will tell us an important point about the effect of $w$ on the outcome.
If $U$ is unmeasured, then this means that the effect of $w$ on $y$ is itself confounded since there is an open backdoor $w \leftarrow U \to y$.  This is an important point, because while the effect of $w$ may be confounded, then effect of $x$ is not.
What does this mean for you?

My question is that if birth weight differs between the groups, can that affect or be the reason that it is significant for the outcome? Can some bias have occurred?

Yes, I think so.  If there are unmeasured confounders $U$ which cause low birthweight $w$, and low birth weight $w$ in part causes disease $x$, then simply adjusting for $w$ in the regression may yield a biased estimate of the effect of $w$ on $y$ due to the open back door.  Depending on the direction of the bias, this could yield a significant result.
There is also the issue of practical significance, which I will not expand on here. My answer comes primarily from a causal perspective.
Here is an applied example.  I've simulated data from the dag above and conducted a regression on each simulated dataset.  I've plotted the effects in a histogram, with a red line to indicate the true value

Note that the effect of $x$ is unbiasedly estimated, where as the effect of $w$ is biased (and hereto the intercept due to $U$ not being included in the regression).  Below is code to reproduce the figure
library(tidyverse)

dgp <- function(x){
  
N <- 250
U <- rbinom(N, 1, 0.5)
w <- rbinom(N, 1, 0.5 + 0.2*U)
x <- rbinom(N, 1, 0.5 - 0.3*w)
y <- rbinom(N, 1, 0.5 + 0.1*x  - 0.1*w - 0.2*U)
d <- tibble(x, y, w, U)
d
}

data <- rerun(1000, dgp())

models <- map(data, ~lm(y~x+w, data = .x))

coefs <- map_dfr(models, ~{
  broom::tidy(.x) %>% 
    mutate(
      truth = case_when(
        term == 'x' ~ 0.1,
        term == 'w' ~ -0.05, 
        T ~ 0.5
      )
    )
  }, .id = 'sim')


coefs %>% 
  ggplot(aes(estimate)) + 
  geom_histogram(bins = 20) + 
  geom_vline(aes(xintercept = truth), color = 'red')+
  facet_wrap(~term) + 
  theme(aspect.ratio = 1/1.61)


A: The crucial issue is surely the effect of treatment. If that remains substantial even with birth weight in the model then you can explain to the readers that the observed effect of treatment on development was over and above the effect of birth weight. Another way to look at it is to think that having entered birth weight into the model any other variable is predicting the residual of development given birth weight so you have removed birth weight.
This all applies to regression in general, it is not specific to logistic regression.
