4400kg on a -400 is about 5% of MTOW, whether there is issues depends on a variety of things. If it was flying sluggish on 2 engines, think what it would be like on one accelerating from a few knots above V1. Then you have issues like Zero Fuel weight and the impact of overloads over a number of flights over time affecting fatigue life, gear limits, brakes and hydraulics, who knows, maybe pickle forks. If one flight departs accidentally over weight every now and then there is not much chance of the holes lining up, however the more often it happens the more likely we get answers to the questions posed in worst case scenarios.
Its a bit like saying there's nothing wrong with a truck being overloaded, until you have to brake suddenly to avoid an accident, or start down an steep descent and find the brakes fade out. Or engine and drive train wear out at half life because they have been working overtime.