How can I carry more than 15 kg luggage on a domestic flight?

Well, there are multiple workable and tested options. However these are subjective and won`t necessarily work every time:

Simplest and Ethical, Buy extra piece of luggage while booking ticket, its cheaper and safest with no worries in future.
Carry all dense, heavy stuff in carry-on luggage. Generally its not weighed but sometimes it can be, specially if its a small plane and weight constraints are high.
Jackets, they are the travellers companion. You can stuff quite a lot of things and no one checks the weight of you jacket.
Multiple clothing, wear multiple yet manageable layers of clothing till you cross the security or board the flight. Later you can remove it in the flight.
Duty Free bags, Though have never tried it, people say they stuff their things in duty free bags which are generally not checked while boarding.
Finally, be friendly with ALL of the staff, be submissive and not demanding, some of your excess kgs can be waived off.
Note: Sometimes airline measure the weight of passenger with the bags before boarding, specially if its a small plane like Embraer RJ135 or sea planes, its a risk.