Two of the guest bedrooms in my house are under the same circuit breaker trip switch. I just found out that I can't have a 1500W room heater plugged inside each of those bedrooms at the same time, as the circuit breaker trips when I do that. This is inconvenient as we use room heaters at night in the bedrooms we use to save on electric bill. Is there a way I can easily & safely "adjust" the circuit breaker so raise the "trip threshold" just enough so that it does not trip with the 2 heaters on? Or is this a job that will require rewiring the 2 rooms?
Conventional residential circuit breakers are safety devices that are not subject to adjustment. They are sized based on what the wires to the outlets can safely handle.
As you surmised, if you want to draw more power to that area, you need more wiring.
This is inconvenient as we use room heaters at night in the bedrooms we use to save on electric bill.
Electric resistive heat is the most expensive way to heat a home. If your central heating method is electric resistive heat then using unit heaters will not save you anything. KWh's are the same whether they come from the central heat or the unit heaters. If your central heat is natural gas, propane, or heating oil, then you are wasting your money with electric heaters since the other methods are much cheaper.
As bib points out, standard home breakers are not adjustable and the only way to increase capacity to that area of the home is to add at least one more circuit.
If you can't increase the wattage available in the rooms (which requires running more circuits as others explain), apply the heat more tactically. Heated blankets or mattress pads can provide more comfort for less wattage than room heaters.
You could always run an extension cord to another room that is on another group/breaker. But that does not solve your real problem either: that you can't heat your house the way you want to.
You did not mention what type your regular heating is. If it affects your electricity bill then it is presumably a heat pump, which has a far greater efficiency (COP) than a resistive heater. The only problem is that it heats up the rest of the house too. Some of that is desired, you don't want to have breakfast in an iglo. But, does it work with air or circulating water ? Because if it is water then there is a nicer solution.
I have a Honeywell Evohome system where the temperature in each room is regulated individually, even if it is the only room in the house that requests heat. This is an extreme form of zoning. There exist also heating systems with only 2 zones, where you can control 2 floors separately, with 2 thermostats. I have (almost) as many thermostats as there are rooms. If any room requests heat then the central controller turns on the gas furnace but keeps the radiator valves for the other rooms closed. I'm not saying that I am saving any gas, but the comfort has increased tremendously, especially in the bathroom. It is warm long before the room where we have our breakfast.
And yes, I installed it myself (this is DIY). Not recommended by Honeywell, but I used to be handy. It isn't too hard if you have hydraulic and computer skills. It's much more expensive than installing an extra breaker, though.
The wiring could be sufficient to allow for higher current. it is technically possible, and allowed, to fit a circuit with a breaker with a lower treshold current than that the wiring can take.
But before you think of replacing the breaker with one >15A, you would have to look at the wiring - depending on your location and legislation, have a certified professional do that.
Under no circumstances increase a fusing current beyond the current the circuit protected by it can take.
If the two rooms do have separate circuits that happen to be wired to the same breaker inside the panel, separation and a second breaker could solve the problem as long as the overall current capacity of the panel (one of its phases) is not exceeded.