I almost exclusively use Combat Armor all the time, and I've also been hoarding it to equip my settlers with it. I think it's the most well balanced and the best looking armor in the game. Settlements like The Castle feel much more like actual military posts when everyone is walking around in matching Military Fatigues and Combat armor. Once you hit level 35 or so, the basic Combat Armor and the Sturdy Combat Armor starts becoming pretty common. I'm at level 51 now, and I've been hoarding them both ever since they started becoming more common. I'm at the point where I have around 40 full sets of Combat Armor and another 20 or so full sets of Sturdy Combat Armor, in addition to another 40 or so random pieces of modded combat armor. However, the Heavy Combat Armor has remained fairly elusive. I've found a few random pieces of it around, mostly on Gunners, but I was still two pieces short of having a full set of Heavy Combat Armor. I had the chest piece, the left arm, and the right leg.
Earlier today I found out that I already had the missing pieces. All of the variants of the Combat Armor share the fact that mods can be switched from one type to another. This is very useful. If you have a modded set of regular Combat Armor and then upgrade to Sturdy Combat Armor, you can just remove the mods from one and attach them to the other. However, when mods are added, the names of the armor components cease to designate whether it's regular, Sturdy, or Heavy.
For example - Suppose you add the polymer and deep pocket mods.
On the regular Combat Armor, the name becomes Deep Pocketed Polymer Combat Armor.
On the Sturdy Combat Armor, the name becomes Deep Pocketed Polymer Combat Armor.
On the Heavy Combat Armor, the name becomes Deep Pocketed Polymer Combat Armor.
Needless to say, this can create a bit of confusion. Although these three different armors all have the same names after being modded, they have significantly different damage resistances and weights and such. But without more closely inspecting them, you can't tell which is which. A lot of the Combat Armor I've picked up off of enemies has been modded already, so the names didn't necessarily reflect what variant it was.
Earlier today I was switching the mods on my Sturdy Combat Armor. I usually use the Deep Pocketed mod for increased carrying capacity, but I wanted to try out the Shadowed mods for increased stealth. Since I had all of these random pieces stored, I decided to just remove the mods from other pieces rather than building new mods. So I pulled out the necessary pieces and went to the armor station. I'm breaking down a Shadowed Reinforced Combat Armor Right Arm...and what do I find after breaking it down? It was a HEAVY Combat Armor Right Arm. This is one of the pieces I was missing. So I did some searching and managed to find the left leg that I needed to complete my set of Heavy Combat Armor. I went through and removed the mods from the rest of my inventory of modded Combat Armor, and I now have three full sets of it, and a fourth set that's just missing a right arm.
So, like I said in the title, if you've stockpiled Combat Armor but you're still looking for that elusive Heavy Combat Armor...you just might already have it.
On a related note, the Combat Armor Helmet seems to be incredibly rare as well. I've been looking for one for the entire time I've been playing the game, which is about 180 hours now. I finally found one earlier today on a raider during the Jack Cabot mission. I was ecstatic. Then after that I figured it was finally time to go check out Covenant (that's an odd place), and I went and looked through the merchandise at the store..and what do I find? Destroyer's Helmet, which is a Legendary version of the Combat Armor Helmet that grants +1 Charisma and +1 Intelligence. It was just after completing the 'Human Error' quest at Covenant that I discovered that I already had the Heavy Combat Armor. It's been a good day in the Fallout Universe for me.
Regarding the Destroyer's Helmet at Covenant -
I edited the last part of my post because I realized there was a bit of a spoiler in it. Sorry about that.