On every file change ST status bar says - indexing files. And it takes > 10s (I have a lot of files). When it does that - 2 CPU cores are loaded at 99%.
Opened the console (@jskinner suggested to enter sublime.log_indexing(True)) and there was a message that index is corrupted and I have to remove it. Index is located in:
/Users/bumbu/Library/Application Support/Sublime Text 3/Index
Removing all the files from that folder did the trick.
http://www.sublimetext.com/forum is a better place for this, but as a stopgap you can disable file indexing via the index_files setting. You can also find out more about what indexing is taking place by entering sublime.log_indexing(True) in Sublime Text's console.
For me it was trying to index a huge folder containing images, you can use project settings to exclude some folders with the folder_exclude_patterns setting.