2.4GHz Bluetooth PCB Trace Antenna Range
Copying an antenna design is hard, it won't work first time even if you keep all dimensions the same. Variations in the PCB dielectric coefficient will change the tuning.

Tuning the transmitter is different from tuning the antenna - the transmit frequency you're measuring is fixed by the crystal oscillator. The antenna is a filter that's independently tuned, and with your test equipment you can't easily sweep it, so you need to tune for best performance at your chosen frequency.

Fortunately its easy to tune the antenna, by cutting and/or extending it. This is the normal process when porting an antenna design to a new PCB, or even just changing PCB manufacturers or board suppliers.

Cutting process Try cutting the tip of the antenna shorter, 0.5 mm at a time. If the results get better, keep going, otherwise extend the track with some wire or copper tape, and start trimming again.

Measuring your results Set up a measurement so you can tell how you are doing, either use the two modules talking to each other, measure the RSSI or measure the range, which is much less accurate. Or measure the transmitted power with a spectrum analyser and a standard antenna. Keep the board under test close to the receive antenna. Rotate the board to get the maximum signal. Then you can start trimming, always measuring in the same position.

If you're going into production with the board, you'll need to control the dielectric. Specify the PCB material carefully, insist that it's from the same batch, etc. You can also keep some spare pads for tuning, zero ohm jumpers, a second capacitor pad in the tuning network, or some other way of adjusting the impedance on an existing board.