MyAppSharer is a nice application which helps you in the process of sharing your installed application with other people. It comes with a friendly user interface in which you can see a full list of apps installed by you. Towards the upper part of the window you will find a search box that makes your life easier when looking for a specific application.
There are two ways for sharing a package with somebody else. You can either give your friends a link towards Google Play or the actual APK package of a certain application. MyAppSharer provides support for sharing this data using Facebook, Bluetooth pairing, QR-Code, Gmail, and a couple of other methods. In addition, this tool can be used for backing up your important APKs to a SD card, as long as you have one present inside your Android device.
In case you plan to share your APKs using Dropbox or QR-Code you'll need the official Dropbox app and a barcode scanner. This software is very lightweight and it runs on your smartphone without using too many system resources. It should work fine even if your device is not that powerful.