There are several assembly languages, not just one. Fortunately, with AI, I found the one you're referring to.

https://www.yorku.ca/sychen/research/LMC/LMCInstructions.html

LMC is Little Man Computer, which appears to be a minimalist assembly used for education purposes devised in the mid 1960s (there's a Wikipedia article). It only has 9 instructions while real world assembly tends to have maybe 100 instructions and some, significantly more.

In particular, the command BRz is "branch if the value of the accumulator is zero to an absolute address". Normally, there's a branch that depends on a register, but when you have an accumulator, you basically have two registers: the accumulator to compute stuff and the PC which is the address of the currently executing instruction. The BRz looks at an accumulator, checks if it's zero, and sets the PC to the hardcoded label or address if it is zero, causing the PC to do something besides incrementing up to run the next instruction in memory.

MIPS, an actual assembly language, has a similar branch instruction which does relative branches but has more flexibility (because it supports 32 registers, instead of 1 accumulator), but it's still a fixed offset to PC like LMC. It does, however, have a JR command which is jump register which loads the PC with the contents of the register, so you could branch to a 'jr` command and the register would contain this word size as a kind of variable.

OK turns out you're not using LMC but a variant called LC-3 which has 8 registers instead of an accumulator.

The commands include BRz as mentioned earlier that still behaves the same, but there is also BR which is what MIPS calls a jump command. Branch commands typically test a register (or two) and jump relative to some address (in this case, it tests if a register has the value 0 and jumps if it does).

A jump command does not test a register. However, LC-3 says the br command is an unconditional branch, so it behaves like a branch.

If you were to write it in pseudocode, you want it to do something like

  BRz R1 L1
  BR X # X would be one of your two word sizes

L1: BR Y # Y would jump based on a different word size

Basically, you're trying to implement something like

if R1 is zero: 
   goto Address 1
else:
   goto Address 2

MIPS would allow this to be easier by using a jr command where the register could contain the size, but you have to construct an assembly version of if-else and possibly more than one if-else.

At least, that's the idea that comes to mind.

Here's a sample LC-3 program: https://github.com/dideler/LC-3-Programs/blob/master/characterCounter.asm

Here's Wikipedia on it: https://en.wikipedia.org/wiki/Little_Computer_3

I would look at sample LC-3 code for implementing something like if-else to get you started.