I know the weights are different, but I don’t really understand how, exactly, they differ. Is there any way, for example, to adjust the weights to try to combine 1-year files into something comparable to the 3-year estimates? What are likely to be the problems with such an approach? Are the replicate weights less susceptible to these problems than the household or person weights?
It is possible to create your own 3-year estimates for the ACS. The multi-year files are simply a concatenation of the single-year ACS data files, which means you can select the three years you are interested in from the IPUMS-USA selection menu, adjust the dollar values to the most recent year in the 3-year set (using YEAR and the CPI99 variables), and divide all weight values by three. While the Census Bureau does use more complex methods for generating multi-year weights (see Weighting Methodology from the 2012 3-year Accuracy Statement), simply dividing by three is the primary adjustment and provides extremely similar values to the Census Bureau calculated weights.
To test this combination method, I would recommend replicating an analysis using a three year period of the ACS that already has a 3-year summary file, such as 2010-2012. You can construct your own 3-year file and then compare your results to those already published to assess where there may be differences.
I hope this helps.