[jeffreyH (OP)]

Is there such a thing as heavy ammonia in the same way we have heavy water?

[chiralSPO]

Is there such a thing as heavy ammonia in the same way we have heavy water?

Certainly!

Deuterated ammonia, ND₃, is commercially available, and is often used for isotope labeling studies. Presumably NT₃ is also used for some things, but that's radioactive, and I don't do any radiochemistry!  ¹⁵NH₃ also exists.

[chiralSPO]

Cambridge Isotopes sells isotopically labeled things of all kinds, largely deuterated compounds.

http://www.isotope.com/products/index.cfm#

I use deuterated solvents routinely for conducting NMR experiments, and occasionally for studying mechanisms by comparing rates (kinetic isotope effect) or seeing where D is incorporated in a molecule (and using that info to gain insight on intermediate species).

[Bored chemist]

If you are prepared to pay, you can get the deuterium  substituted version of just about anything.
Deuterated versions of compounds are often used as standards in chemical analysis.

[adianadiadi]

Heavy ammonia is represented by ND₃. What is special about this is, instead of normal protium isotope of hydrogen, ¹H₁, there are deuterium isotopes, ²H₁, also represented by D. The MW is 20 g mol^-1. That is why we call it heavy ammonia. Normal ammonia's MW is 17 g mol^-1.