Perhaps yes, this could be done. But it would be a very large reactor, which woulld be heavy. Read carefully this link:
That thread is kind of confusing. There's a lot of stuff about plutonium and space reactors. The formula I assume I'm supposed to look for eludes me.
What I found much more helpful was to study the integrated SMR designs I intend to use as the basis for the reactor plant. Looking at several designs across multiple sources, it seems that a reasonable power/weight estimate would be an 80-100 MWe reactor weighing around 650-750 tons at power. Of course, one has to factor in the system around it as Heuhen mentioned, but a lot of this would also apply to a conventional powerplant, with the exception of perhaps the electric turbine. By comparison, a single Wärtsilä-Sulzer RTA96-C diesel engine weighs upwards of 2,000 tons, plus around 18-20,000 tons of HFO on the largest vessels (and it appears these fuel tanks aren't exactly small
), which would no longer need to be carried on a nuclear vessel.
I don't know the exact totals of each (conventional and nuclear) in terms of weight, and I may well be missing something, but a cursory look at the main components involved (installed power and fuel load, assuming similar "guts" around each and adding a turbine for the nuclear plant) suggests that the weight of a reactor plant wouldn't pose any major issues, and might even end up saving weight.
I should note that the only design where I'm looking at installing two reactors is the 20,000+ TEU class. These are larger and heavier than even aircraft carriers, which already use two reactors.