When adding the ModuleKISInventory module to a part, the part will increase in mass in game. The game's mass reporting mechanisms will most likely not show the real mass, but MechJeb2 does. I have tested this bug without any other mods installed besides KIS, and here's how:

Build a rocket with the Okto2 probe, Jumbo 64 Fuel tank, and Skipper engine. Without KIS being added to the Jumbo 64, the whole rocket will take off easily from the launch pad. Adding the KIS inventory module to the Jumbo 64 will increase it's mass from 36 to 68 tons. This will put this rocket under 1 Thrust to Weight ratio, meaning that when you launch it, it will sit there till enough fuel has been burned off to increase the TWR above 1.

Here's the module being added to the Jumbo 64:

MODULE
{
name = ModuleKISInventory
maxVolume = 1
externalAccess = true
internalAccess = false
slotsX = 6
slotsY = 4
slotSize = 50
itemIconResolution = 128
selfIconResolution = 128
openSndPath = KIS/Sounds/containerOpen
closeSndPath = KIS/Sounds/containerClose
defaultMoveSndPath = KIS/Sounds/itemMove
}

(maxVolume 1 or 1000 actually doesn't matter)

The amount of mass being added seems to correlate to the amount of fuel the part holds. The more Fuel, the more mass added.

Here's the output log from the test with KIS installed on the Jumbo 64: https://www.dropbox.com/s/wbllpv8qh4gazr5/output_log.txt?dl=0

System specs:
Windows 7 pro 64 bit
AMD FX 6300 six-core 3.5 ghz
16Gb Ram
Nvidia GTX 660ti
Kerbal Space Program 32 bit "Steam edition"

I noticed this issue when I added KIS to the Descent stage of the FASA LEM. I ran out of fuel when trying to land on the Mun. After some investigation, found out that the Descent stage fuel tank had more mass than it's supposed to thanks to KIS.