I can see how you have problems if your device only has 2Gb of storage.
The size of the apps are determined by two factors: app size and data/cache size. The app size is the size of the app code and its data. How much space this takes up is determined by the developer.
Data is the actual app data and cache consists of temporary files that can be deleted any time. Clearing your cache will not delete user accounts or settings. Clearing data can.
If the 'data' part of the apps is taking too much space, you should enable Chrome sync. This will sync all history/bookmarks and some settings across your devices, so if you clear the data after syncing your data will appear again after logging in again.
This does not solve the problem of storage shortage, it will only delay it. You have root, and this page says you can insert a MicroSD card into your phone so Link2SD might be an option.
If you have an external SD card about 4GB+, you can easily extend the amount of storage your apps can use by using an app like Link2SD.
Link2SD (and similar apps) allow you to reserve some part of your SD-card for app storage by allow you to use an ext2/ext4 partition as data storage. You can follow any tutorial like this one or this one to set it up. You don't have an HTC device so you can ignore the S-OFF stuff. Most tutorials will guide you every step, but it all comes down to this:
- Always make backups of everything just to be sure
- Install Minitool Partition Wizard and insert your SD-card into your computer
- Resize the existing FAT32 partition of your SD-card to create some space for apps
- Create a new primary, ext2 partition in the free space (some tutorials use ext4 but ext4 is less fit for solid state storage like SD-cards)
- Install Link2SD and select the new partition when you are to select one
Keep in mind that the ext2 partition will be reserved and no non-app files can be stored in the reserved space (like photos, music, videos). Also, any apps on the SD-card will be gone if you boot your device without an SD-card. If you have a cheap/bad SD-card apps will be a lot slower than when they ran from the internal storage. Use class 8 or higher SD-card for the best results.