Are weather-reporting requirements for an airport in Class D airspace more stringent than for an airport in surface-level Class E airspace? In the US, are weather-reporting requirements for an airport in Class D airspace more stringent than for an airport in surface-level Class E airspace?
Are there other requirements that would cause an airport with an operating control tower to be eligible for surface-level Class E airspace but not for Class D airspace?
The intent of the question is to understand why any airport with an operating control tower, whether &quot;temporary&quot; or otherwise, would have surface-level Class E airspace rather than Class D airspace during the hours that the tower was operational, if in fact this ever occurs-- apart from the obvious case of a temporary (or new) control tower going into operation in pre-existing surface-level Class E airspace.
Related ASE links: In the US, are there any operational control towers located in surface-level Class E airspace or in Class G airspace?
This outside link appears to describe the establishment of temporary surface-level Class E airspace concurrent with the establishment of a temporary control tower-- but may just be an example of inaccurate or unclear writing.  The surface-level airspace at this airport is normally Class G, and the same was true in 2016.  The only NOTAM turned up during an archive search for this airport at this time references the temporary control tower, but no temporary change in airspace designation.
Your First Question: In the US, are weather-reporting requirements for an airport in Class D airspace more stringent than for an airport in surface-level Class E airspace?
Answer: The &quot;Primary&quot; airport within active Class D airspace requires (Ref: FAA Order JO 7400.2M, paragraphs 17-2-9 and 17-2-10:

That a Control Tower be currently in operation;
That a certified and approved weather observation and reporting system (for the primary airport) be in place and operational; and
Communications capability must exist down to the runway surface area (for the primary airport).

However, a primary airport that is within the surface area of active Class E airspace will not have a Control Tower currently in operation.  (if there are airports with a currently operating Control Tower within the surface area of active Class E airspace, I am unaware of them).
With respect to your specific question above, if the airport in question (within the surface area of active Class E airspace) is meant to accommodate instrument procedures (e.g., instrument approaches, IFR arrival/departure procedures, etc.) then the exact same requirements (Ref: FAA JO 7400.2M, paragraph 18-1-3) for communication and weather observation/reporting must be available as are required for Class D surface airspace. (But there will not be a Control Tower operating)
There are a dwindling few airports that have Control Towers that operate while the airspace is designated as active Class G. But, as I mentioned above, the same is not true for primary airports located within the active surface area of Class E airspace. In that case, the Control Tower, if there is one, is not operational (e.g., closed/not staffed - usually in the later evening as traffic warrants).  If the Control Tower was currently operating the active surface airspace would be Class D.
Your Second Question: Are there other requirements that would cause an airport with an operating control tower to be eligible for surface-level Class E airspace but not for Class D airspace?
Answer: Again, as mentioned above, if the primary airport has a currently operating Control Tower, the active surface airpace would be Class D (or in a few cases Class G), not Class E. Therefore, parsing the eligibility requirements between Class E and Class D airspace, both of which (with respect to your question) might have operating Control Towers, is not possible.
Typically, when/if the Control Tower closes (not staffed/closed for the night) at a primary airport in Class D surface airspace, then that airspace surface area reverts to Class G or Class E.
Lastly, my response above excludes special occasions where a temporary Control Tower may be operating in active surface airspace designated as Class E.  This would be a circumstance where a NOTAM or similar would exist identifying a particular event taking place.