If you have a look at the engine placement in a top fuel dragster, the engine is ahead of the rear wheels however behind the driver. There is little to no weight "up front", most weight is behind the vehicle mid point and the large majority is also very close the the rear pivot point around the rear axle.
For Funny Cars the engine is ahead of the driver but still behind the front axle line.
As said the main factors are
1: weight distribution (CoG)
2: engine torque
3: tyre traction (stiction)
4: tyre action
Drag tyres are not only bead locked and run lower PSI, but they are called "wrinkle walls" for a reason. The side wall is very soft and under initial loading they twist and wrinkle up acting like a spring. This softens the initial torque loading and limits traction loss. As the car starts moving they unwind releasing the energy stored in the tyre.
This action allows the tyre to maintain grip and then releases the torque in a controlled manner.
If the tyre has enough "stiction" then the action of tyre will see the car car will try and rotate around the rear axle as torque is applied.
When this happens either the tyre breaks the stiction threshold and starts to spin, the car overcomes its moment of inertia and starts moving or the action of the torque on the rear axle caused the chassis to start to rotate around this pivot point and lifts the front wheels. Usually it is a combination of all three.
To counter this, drag cars extend the wheelbase (long nose) or effective wheel base (via wheelie bars on the rear on the chassis) to limit front end lift. However, where the rear bars are too stiff or do not extend far enough they can actually reduce the loading on the rear tyres.
Changing the CoG will effect the amount of force needed to lift the front wheels.
Another interesting effect of the wrinkle wall tyres is that as their speed of rotation increases they "stand up" and increase in diameter which changes the final gear ratio allowing a higher top speed.
F1 cars have a much lower CoG, lower torque and less grip. The physics just isn't there to lift the front end of an F1 car.
Never approach a Bull from the front, a Horse from the back, or an Idiot from any direction