Use the test proposed in Pfeffermann and Sverchkov (1999) to check whether a regression model is specified correctly without weights.
pf_sv_test( model, data = NULL, weights, sims = 1000, digits = getOption("jtoolsdigits", default = 3) )
model  The fitted model, without weights 

data  The data frame with the data fed to the fitted model and the weights 
weights  The name of the weights column in 
sims  The number of bootstrap simulations to use in estimating the variance of the residual correlation. Default is 1000, but for publications or when computing power/time is sufficient, a higher number is better. 
digits  An integer specifying the number of digits past the decimal to
report in the output. Default is 3. You can change the default number of
digits for all jtools functions with

This is a test described by Pfeffermann and Sverchkov (1999) that is designed to help analysts decide whether they need to use sample weights in their regressions to avoid biased parameter estimation.
It first checks the correlation of the residuals of the model with the weights. It then uses bootstrapping to estimate the variance of the correlation, ending with a ttest of whether the correlation differs from zero. This is done for the squared residuals and cubed residuals as well. If anyone of them are statistically significant (at whatever level you feel appropriate), it is best to do a weighted regression. Note that in large samples, a very small correlation may have a low pvalue without a large bias in the unweighted regression.
Pfeffermann, D., & Sverchkov, M. (1999). Parametric and semiparametric estimation of regression models fitted to survey data. Sankhya: The Indian Journal of Statistics, 61. 166186.
Other survey tools:
svycor()
,
svysd()
,
weights_tests()
,
wgttest()
# Note: This is a contrived example to show how the function works, # not a case with actual sammpling weights from a survey vendor if (requireNamespace("boot")) { states < as.data.frame(state.x77) set.seed(100) states$wts < runif(50, 0, 3) fit < lm(Murder ~ Illiteracy + Frost, data = states) pf_sv_test(model = fit, data = states, weights = wts, sims = 100) }#>#> #> PfeffermannSverchkov test of sample weight ignorability #> #> Residual correlation = 0.157, p = 0.373 #> Squared residual correlation = 0.250, p = 0.144 #> Cubed residual correlation = 0.000, p = 0.998 #> #> A significant correlation may indicate biased estimates #> in the unweighted model.