The weep hole is still used. Chances are that is where it is coming from and then spinning on the belt. Keep in mind, you need to make sure it isn't a rad hose coming to the pump or the intake above.
Here is what I suggest, Fill the coolant level in the vehicle. Then, pressure test it. You may need to use a mirror to see everything, but you should be able to work on it when the engine is cool and system pressurized. Here is a link explaining how it is done:
You may find this link of interest as well:
Now, I realize most people don't own a pressure tester, but often times a parts store will lend or rent one to you,
If you determine it is the water pump, here are the directions. I have to be honest, it isn't a hard job on this one. I did it on my 4.7 (same design) in about an hour.
2003 Dodge or Ram Truck RAM 1500 Truck 2WD V6-3.7L VIN K
Vehicle Engine, Cooling and Exhaust Engine Water Pump Service and Repair Procedures
WATER PUMP - 3.7/4.7L
The water pump on 3.7L/4.7L engines is bolted directly to the engine timing chain case cover.
1. Disconnect the negative battery cable.
2. Drain cooling system.
3. Remove fan/viscous fan drive assembly from water pump. Do not attempt to remove fan/viscous fan drive assembly from vehicle at this time.
Warning: constant tension hose clamps are used on most cooling system hoses. When removing or installing, use only tools designed for servicing this type of clamp. Always wear safety glasses when servicing constant tension clamps.
Caution: A number or letter is stamped into the tongue of constant tension clamps. If replacement is necessary, use only an original equipment clamp with matching number or letter and width.
4. If the water pump is being replaced, do not unbolt the fan blade assembly from the thermal viscous fan drive.
5. Remove the radiator fan.
6. Remove accessory drive belt.
7. Remove the lower radiator hose clamp and remove the lower hose at the water pump.
8. Remove the water pump mounting bolts.
Caution: Do not pry water pump at timing chain case/cover. The machined surfaces may be damaged resulting in leaks.
9. Remove the water pump and gasket. Discard gasket.
Clean the gasket mating surface. Use caution not to damage the gasket sealing surface.
Inspect the water pump assembly for cracks in the housing, water leaks from shaft seal, worn bearing or impeller rubbing either the pump body or timing chain case/cover.
The water pump on 3.7L/4.7L engine is bolted directly to the engine timing chain case cover.
1. Clean the gasket mating surfaces.
2. Using a new gasket, position water pump and install the mounting bolts. Tighten the water pump mounting bolts to 58 Nm (43 ft. lbs.).
3. Spin the water pump to be sure that the pump impeller does not rub against the timing chain case/cover.
4. Connect the radiator lower hose to the water pump.
5. Relax the tension from the belt tensioner. Install the drive belt.
Caution: When installing the serpentine accessory drive belt, the belt must be routed correctly. If not, the engine may overheat due to the water pump rotating in the wrong direction. Refer to figure for the correct belt routing. Or, refer to the Belt Routing Label located in the engine compartment. The correct belt with correct length must be used.
6. Install the radiator fan.
7. Fill cooling system.
8. Connect the negative battery cable.
9. Start and warm the engine. Check for leaks.
Let me know what you find or if you have other questions.
Images (Click to enlarge)
Thursday, February 13th, 2020 AT 5:49 PM