A few things to consider:
1) Neither Weser nor Elbe were really known to the Romans. They probably knew that there were some large rivers east of the Rhine, somewhere, but that's about it.
2) They didn't know, that a theoretical border on the Elbe or Weser might be shorter/more practical in the long run, since they didn't have cartographic knowledge of central/eastern Europe.
3) There was little of interest for the Romans in Germania. The only known resource worth taking were the lead mines close to the Rhine and they remained roman for the duration of the WRE.
4) The soil on central/northern europe is not suitable for roman agriculture methods. E.g. Wheat could only be grown there after the invention of the heavy plow in the early Middleages / late Antic.
5) Germania was sparsely populated and the population was dirt poor and there was no real social hierarchy like in Gaul, making it more difficult for the Romans to rule and assimilate the local population through local elites.
6) The terrain was more difficult then in Gallia, making it more expansive to build the infrastructure necessary to integrate the region into the Empire.
7) In OTL, the Romas had no problem whatsoever to subdue and control the region militarily, but this was expensive and concentrating a lot of force in one region and probably under one commander always carried the risk of a successful General revolting.
8) Historically, the Romans deemed it more practical to abandon the economical worthless region and keep the locals weak and disorganized by allying with some tribes, conducting military expeditions against others and mostly controlling the flow of metal arms into Germania.
TL;DR: Yes, the Romans could have made the Weser or the Elbe their eastern border, but it would have been expensive, bear the risk of creating a rebellious roman general and would not increase the perceived security or stability of the Roman Empire. If they were to push the border that far and hold on to it, they would need a very good reason to do so.