I'm a bit confused with how the Business Analyst generates the report and infographics. To my understanding and from what I've found on the data section of the BA site, the lowest resolution possible for demographic information is a census block group. However, somehow ESRI and BA, provides a higher resolution which I'm not sure how it is calculated.
From looking at a couple of examples I found that most infographics or reports are calculated based on area and not real data. For example when looking at block group 080350139.014, if I draw a polygon over an area (0.17 square miles) without any houses I get population 547 and 179 households. However if I draw a polygon over a dense residential area (0.09 square miles), I get population 388 and 113 households. So either I'm missing something or these infographics are highly inaccurate unless we're talking about small and homogeneous census blocks.
Not sure if you are working with Business Analyst Web App or ArcGIS Business Analyst Desktop but for the Desktop version census block centroids are used when using the Block Apportionment method. Hybrid is a bit different as when the polygon gets larger in size the centroids used are scaled up (blocks>block groups>tracts etc..) for some additional performance (processing speed).
Below is a Help link to the Data tab in ArcGIS Business Analyst Preferences that details the three apportioning methods that can be selected (Hybrid is the default setting however some clients prefer the most accurate apportionment in using block apportionment at the cost of some performance for large/many areas). The block versus cascading section half way down the page is most informative.
I helped a Business Analyst Desktop client recently where examining block centroid aided greatly figuring out what was going on. So the issue was a simple ring in Miami that was located in a heavily commercial business area but the client found that when running a 2018/2023 data report and comparing it to a 2017/2022 that there was a large jump in population that jumped out and needed an explanation.
After taking a look at the block centroids that are captured by the simple ring found one right on the edge that showed higher population. A google maps/streetview and resulting search showed a brand new apartment complex that opened in late 2016 that the Esri 2018/2023 dataset was able to capture.
For the Business Analyst Web App below is the Help link that details US and international spatial apportionment.