The question asks about connecting point data (measurements of concentrations of a substance in samples of an environmental medium) to areal (aka "lattice") data, which represent aggregate values collected within administrative units.
The objective is to look at relationships among multiple variables. One of them is intended to be some sort of representative summary of the concentrations within each Census unit; all the rest already are attributes of the Census units. Therefore, we need to aggregate the point values to the Census unit level, not the other way around!
To do this, some thought about what the concentrations mean will be useful. Their meaning depends on how they were collected and what is important to know about the environment.
To clarify this point, consider two different situations with the same formal data. In the first one, scientists sample (say) two locations randomly within each Census area. The purpose is to obtain concentrations useful for estimating average concentrations within each area. One would want to use some average, or perhaps weighted average, of the concentrations within and near any Census area to estimate the true average concentration within that area. In the second situation, suppose scientists sample locations thought to be contaminated (such as air near smokestacks or water just downstream of industrial outfalls in creeks and rivers) without regard to the Census areas. (This is a typical application.) Their purpose is to assess extreme (not average) conditions. Due to this focused sampling, some Census areas may include many samples and some may have none. Here, averages could be meaningless (or deceptive), whereas the maximum concentration observed within each Census area might be useful (perhaps leaving Null values within Census areas without data). In other applications, distance-weighted averages of the concentrations might be more appropriate.
Other scenarios are possible, but these make the point that there is no universal, general-purpose answer to "how do I combine these data?".
Nevertheless, in many cases it can be reasonable to do the following:
For each point location, identify its containing Census area (if any). This is done in GIS with a spatial join. This adds a new field to the point attribute table. The field contains a Census unit identifier.
Compute a statistical summary of the concentrations, such as a mean (in the first scenario) or maximum (in the second) for each Census unit. This is done in GIS (or in any database application) with a summarize operation applied to the point attribute table, using the Census unit identifier as the grouping attribute. (At the same time one can pick up auxiliary information, such as counts and variances per Census unit, almost for free: these can be useful in many circumstances for weighting the data in statistical analyses.)
If necessary, join the statistical summaries (of which there will be at most one per Census unit) to the Census unit attribute table.
The resulting attribute table now has a new column representing the points (here, the concentration summaries). It contains all the data needed for statistical analysis, whether it be GWR (which presumably would use coordinates of central locations of the Census units), ordinary least squares regression, or anything else.