How can I determine if my neighbor is hooked into my meter?
You have a tough bit of detective work to do, but it should be possible.  The good news is a very large load is likely to be a continuous load, so it shouldn't be too hard to catch. 

First check for weird outside wires.

The usual drill with pot growers is to bury Romex (NM) cable just enough to conceal it. This shabby workmanship is usually fairly easy to spot. Proper underground cable is at least 12" deep, rigid conduit can be 6" but that's because you won't damage it with a shovel. 

A sneaky cable would explain all this even if they took away their grow lights. (you have inspected the unit, yes?) Imagine they were stealing power from the neighbor, then also stole it from you but hooked it up backwards. It would be a dead short, limited by the long wire run, and that might be enough to not trip the breaker.   

OK, no luck?

Next, get educated.

I know some people don't like learning and don't want to be seen as smart. But frankly, the alternative is pretty expensive.  Upside, this is a big enough deal you can afford a few toys to make learning easier. 


Learn how pressure (volts), current (amps), power (watts and VA) and energy (watt-hours and kilowatt hours) all relate to each other, because you'll be using them a lot.  
You need to be able to multiply and divide.  It doesn't get any harder than that. 
Get a book on wiring a house and read it through.  There are a few things you can skip but the main thing is you need to be comfortable working around wires and inside panels. 
Figure out how to get instantaneous kilowatts out of your electric meter. (smart meters should cycle to display it, old meters are trickier.)
Toy: a $20 "Kill-a-Watt" meter which will let you measure most of your 120V loads. 
Toy: A $100 clamp ammeter which lets you clamp around a single "hot" wire and see what current it is drawing.  
Toy: A "whole-house power monitor" which wires into your panel and analyzes your power consumption.  It shows you exactly which appliance uses how much power, and give you a very complete picture of your power usage.  These are in the $300-500 range and permanently install two clamp ammeters in your service panel. 


Once you are able to easily read your instantaneous watts (e.g. at the meter), you can try flipping off one breaker at a time and try to narrow it down to one breaker.  If your two units have separate panels but are fed off one meter, you may be able to use a clamp ammeter to measure both main hots (one at a time) to see which house is the source of it.  

If an answer doesn't become obvious at this point, you'll need a more methodical approach. 

Map your circuits

This is tedious but very useful to know. You know about all  your hardwired loads (lights, oven etc.), get some dollar store night lights for testing receptacles.  Shut off one breaker at a time and see what got turned off.  Mark the service panel with what things that breaker controls, and mark each device, switch or outlet with the breaker number.   

Next, use the Kill-a-Watt to measure the actual power draw of everything that plugs into a receptacle.  I have been known to measure fixed loads also, by opening up the box and using a stinger extension cord.  You cannot measure 240V loads with a Kill-a-Watt, but then you don't have to - 240V loads have nameplate labels which state their power usage.  You just have to figure how often (percentage of time) the big load is on.   By now you should have a notebook or excel of each of the circuits and the Kill-a-Watt power usage of each of the devices on that circuit.  

Look for anomalies

Now put the clamp ammeter on each of the "hots" coming out of a breaker.  Compare that to the Kill-a-Watt data from your known loads on that circuit.  It can help to just turn those off while you're measuring.  The goal is to account for all the power exiting every breaker. 

For 240V loads, measure both hots separately.  A significant difference in amps should raise alarm bells.  Dryers have been known to be unequal, turn the dryer off and see if it all goes to zero.  

The goal is to narrow the unexplained draw to a single circuit, then tear into the circuit to find exactly where the draw is.  You can follow the circuit down the chain of receptacles and put the clamp ammeter on the hot wire in each receptacle until you find the leakage.  

Be prepared for the possibility that it isn't any sort of theft, but something left on (heater in vacant apartment?) or just appliances that take a lot more power than you thought (air conditioning).