Creating Multi-Year estimates

Since Census Bureau discontinued the 3-year multiyear estimates files in 2014, I'm attempting to create 3-year estimate files for more recent years using PUMS. After contacting ACS support, they mentioned a simple approach of combining the 1-year files together and then divide the weights by 3. And if using the replicate weights, they will also need to be divided by 3. I conducted this simple approach for years 2011 to 2013 as a validation test since 2011-2013-3-year-estimates file was the last file produced from Census. When doing this approach, I get total population count about 1% less (Approx 3 million) from the total population estimated from the Census Bureau 3-yr estimate file. In addition, when I drill down to narrower categories, the percent differences increases around 2-3%. This discrepancy is concerning to me and I am curious if anyone has any recommendations/suggestions on why I am getting this discrepancy and how can I get a estimate closer to what Census got?

ACS support also mentioned using the Population Estimates if I want to do anything sophisticated. However, I am not a survey statistician and I don't have a strong understanding on the weighting process to know the next steps. Any help would be appreciated!