Is data/data/com.android.browser/databases/webview.db being encrypted? I rooted my phone (Galaxy Nexus 4.1.1 JRO03C). I am able to access nearly all files under data/data/* folder. However, a few files cannot be opened, such as data/data/com.android.browser/databases/webview.db

I suspect these files are encrypted. Is there any way to decrypt them?
The database file obviously is not encrypted, see: Browser webview.db doesn't store hotmail password, but I can still auto log-in hotmail. Why? which shows the user was able to read data from its tables. But they are protected using "file permissions" -- so aside from root only the owner (i.e. the app) has full access to them.

You now will probably argue you said having rooted your device. So far, so fine. But did you use your "root powers" when trying to access those databases? Just having your device rooted does not mean all stuff automatically runs with root permissions (see: Do all applications run as root on my phone after rooting?). The app you're using to open those files must itself have requested (and be granted) root permissions -- or they might get either no or only restricted permissions on files they do not own.