Looking for a simple, offline, portable, lightweight IDE for C++ with a compiler and debugger
My department uses Dev-C++. It's free, simple, offline, portable, and lightweight. Windows native.
Over the years the maintainer has swapped hands a number of times, it's occasionally gone a number of years without updates, and the size of the install has increased. But I like it quite a bit. As of this edit it got a new maintainer and update to v.6 a few months ago (November 2020):

Dev-C++ v.6 by Embarcadero (72 MB, 1/31/21)
Dev-C++ v.5 by Orwell (49 MB, 4/27/15)
Dev-C++ v.4 by Bloodshed (9 MB, 10/10/05)

Mirrors for the v.6 version that avoid the current maintainer's request for a lot of personal data can be found here and here.