I am working with DHS (Demographic and Health Survey) data. I have pooled data from about 25 countries taking 2 most recent waves from each country. My dependent variable is neghaz (negative of height for age (cm/months)) which is continuous in nature. My regression specification includes several control variables including square terms and interaction terms. The specification also includes variables that have been calculated at PSU/cluster level (mean employment rate in the cluster, etc). I have certain doubts regarding weighting and clustering.

1. The data has widely varying no. of observations with India having more than 200000 valid observations while African countries only having a few thousand observations. Shall I use weights to perform the regression analysis in this case?
I performed the regression both ways i.e., with applying weights and without applying weights. The standard errors changed significantly. Is the weighted regression a better choice for this analysis? (reg neghaz $controlset [pweight = perweight], cluster(psuid)). The weights that i am using have already been de-normalized.

2. I read on some forums that while pooling data from countries clustering shall be done at country level as well as PSU/cluster level. Some people recommended using fixed effects by adding an "i.survey" to my model specification. On the other hand some people recommended using a hierarchical model to take account of clustering at multiple levels. Which model shall I use for analysis and why? I have read some literature in this regard but i only got confused.

When I ran the regression with an i.survey term both the coefficients and standard errors changed.

I am sorry if my queries sound noobish. This is my first time with pooled data from so many surveys.