The BQE is part of the interstate highway system and allows trucks. In fact a major factor in the deterioration of the cantilever section of the BQE is large numbers of illegally overweight trucks.
https://brooklyneagle.com/articles/2021/06/10/bill-to-id-penalize-overweight-trucks-on-bqe-passes-legislature/
Here is a link to the NYC truck map:
https://www1.nyc.gov/html/dot/downloads/pdf/2015-06-08-truck-map-combined.pdfIf one looks at this very carefully, you can see how difficult it is to legally drive a large truck within NYC. Certainly, they are prohibited from using the parkways. And only a handful of streets are allowed to carry thru trucks in their stead.
And if you are driving a "53 foot trailer" (I imagine this means tractor/trailer) there is only one legal way to drive from NJ to CT, LI, or JFK airport. I belive these vehicles are totally illegal on every other highway/street in the city, but perhaps to meet constitutional muster (local laws not unduly burdening interstate commerce), they provide a very specific truck routing for these routes that, practically speaking, must drive through parts of NYC to avoid gigantic detours.
NJ to Conn: Must stay on I-95 via GWB and Cross-Bronx
NJ to JFK airport: Must use I-95 on GWB and Cross-Bronx and then take the I-678 along the Whitestone Bridge and Van Wyck. This is far longer than utilizing I-278, especially if strarting in central or southern NJ (and by extension most of the rest of the US)
NJ to Eastern LI: Must use I-95 on GWB and Cross-Bronx and then take the I-678 along the Whitestone Bridge and Van Wyck to I-495 east. This is far longer than utilizing I-278 to I-495, especially if strarting in central or southern NJ (and by extension most of the rest of the US)
So while the BQE does allow for trucks generally, the largest trucks are supposed to avoid it and take I-95 instead.