I.e. - Id est. Makes sense. E.g. - Exempli gratia. Makes sense. Etc. - Et cetera. Annoyed. If you dont have to put a full stop after the t in etc, then you shouldnt have to use them in ie and eg.
The full stops are used to indicate contractions. Note that they're not necessarily required. But, in your examples: Id has been contracted to 'i' and est to 'e' - so it's represented as i.e. Exempli has been contracted to 'e' and gratia to 'g' - so it's represented as e.g. Et has NOT been contracted (so no full stop is required) but cetera has been contracted to 'c' - so it's represented as etc.