Firstly, very few tests for differential effects in subgroups of randomized trials are affected in their validity by treatment group or subgroup size imbalance (they may of course be affected in other ways, e.g. power). The most natural test would be those based on suitable regression models (e.g. linear regression for continuous outcomes that don't need transformation, logistic regression for binary data, negative binomial regression for count data etc.) adjusting (or stratifying) for study (but assuming numbers are not too small something like a regression model using effect size by subgroup with the standard deviation fixed to be the standard error adjusted/stratified for study would probably also work).
However, whether such an investigation of subgroups is reliable is more of a question. Firstly, remember that you need way more data to look at subgroups (but with a meta-analysis of many studies, I suppose there is at least hope that you could may do something meaningful). Secondly, non-pre-specification, data-driven selection of the subgroup(s) to look into/the direction of the effect of interest and researcher degrees of freedom in how analyses are done (e.g. definition of subgroups, model/test to use etc.) lead to huge potential for false positive findings.
