The “Small Size Rule” is a homebrew house rule because I didn't see anything, at least with a brief search in the PHB and DMG that clarified small creatures using weapons & armor that would appear visually daunting to them. So here is some clarification on how we're going to deal with these things in D&D 5.5e until someone points out an official or better way that's agreeable. We'll use a Hamsterfolk named “Dave” as an example of a small creature being portrayed as humanoid enough that this is relevant.
TWO-HANDED weapons that are also marked as HEAVY can be used but only at DISADVANTAGE. As an example lets imagine Dave, our Hampsterfolk, trying to use a GREATAXE. That just isn't going to go well. It's going to be top heavy and perhaps try to topple him while he uses it.
This rule shall apply regardless of class, background, misc temporary spell effect or feat implying otherwise.
In a perfect scenario, Dave would not even being trying to justify the use of a Heavy Crossbow. He's have made other choices.
HEAVY ARMOR should be completely banned for small creatures UNLESS they find a specialized small version of heavy armor. If Dave our Hampsterfolk tried to put on standard PLATE ARMOR taken off a dead bandit, he'd just topple over, end of story. However if Dave found a special Plate Armor specifically made for Hampsterfolk size wise, that'd be acceptable.
In a perfect scenario, Dave would not attempt to use a SHIELD while wearing anything greater than LIGHT ARMOR because weight + awkward size of him being small just make it weird logically speaking. For the record Dave would also not attempt to use a shield with most weapons, because that's essentially making everything a difficult two handed scenario for him. I'm sure there are some logical arguments to the contrary forthcoming.