I have tried to perform a propensity score and the number of units in the treatment group is greater than that of the control group, with about 20% of controls in my data. For this reason, we are using weighting approachs (IPTW, Kernel). I also assess balance on my matched data set and I have achieved strong balance. Are there other assumption that I need to control? I am yet wondering that if there is any caveats about doing this? Any papers for reference regarding the amount of controls for weighting methods?
It doesn't matter that there are more treated than control units. There are likely no papers about this because it is not theoretically relevant. The only thing it prevents you from doing is matching without replacement, and that's not a theoretical issue; that's just a matter of the definition of the method. It's just one of many ways to compute an average treatment effect (and it only targets the average treatment effect on the treated [ATT], which may not be your estimand of choice). There are several other methods you can use, like matching with replacement, IPW, propensity score subclassification, full matching, g-computation, etc.
You need to be clear about your estimand (i.e., ATT vs. ATE vs. something else) and choose a method that is appropriate for that estimand and that is compatible with your data. Nearest neighbor matching without replacement is not appropriate for the ATE and is not compatible with your data, but all ATE-compatible methods will be compatible with the relative proportion of treated and control units in your dataset, and most ATT-compatible methods (other than matching without replacement) will be, too.