I wouldn't say that it overheats but the needle goes a bit pass the half mark?

Its leaking somewhere. Let vehicle cool down, open rad cap and fill to top, also refill the overflow jug. Let car idle and watch temp gauge and look under car for leaks. The coolant gauge should move up until the coolant fan comes on then it should come down and fan should turn off. If the fan continues to run and temp rises then we need to dig deeper.

Where is the water going to? Its probably being burn in the combustion chamber.

Have it block and pressure tested-do the block first to pinpoint a combustion leaking into the cooling system or a gas analyzer to sniff for hydrocarbons at the radiator fill neck.

Pressure test: do not do a pressure test if there's leakage at the headgasket this might cause coolant into the cylinders and lock it up or bend a connecting rod if cranked thereafter. The headgasket should be repaired before doing the pressure test.

If the block and pressure test passes check the following: Thermostat, Pressure test the Rad. Cap, Clogged radiator, Fan clutch, Radiator electrical fan, collaspe hoses, water pump.

Did you open the bleeder screws when you refilled it the system. These can be a real booger to get the cooling system to bleed out. That would be the first thing I would do is bleed it out. 2.2 are really bad for not bleeding out correctly, air gets caught in the heater core because it sits lower than the engine. Most likely this is your problem