Without seeing your graph editor curves nobody can tell you much, but generally you should simply get used to the fact that good animation timing takes years of practice and experience. Simply keep refining and tweaking your curves...
I'm new to After Effects, so I get what you mean about good animation timing taking years of practice. I will have to look at the Graph Editor, and photo a photo it on this page.
AE is actually scaling 'correctly' - in a linear fashion, but it will look wrong. Here's why:
Let's say in the first second the aircraft goes from 100% to 500% - 5x bigger
Later in the animation it goes from 2000% size to 2,500% - 1.25x bigger
The scale value is increasing at an even rate per second as far as after effects is concerned - but these units are percentages - that's why the increase in scale appears to 'slow down'.
Here's the solution:
Select your two scale keyframes.
Right click (to get the contextual pop-up menu) and select:
Keyframe assistant > Exponential scale.
This will generate an exponential curve that will give you a perceptually correct increase in scale.
The downside of this method is that it gives you a keyframe on each frame.
(An option to workaround the keyframe-on-every-frame solution is is to duplicate your aircraft layer and apply the above method to the first layer. Then select all the scale keyframes on both layers. Go into the graph editor and use the handles on the keyframes of the second layer to copy the shape of the curve on the first layer. If you don't see handles on the two keyframes of your original animation in the graph editor, select the two keyframes and hit the third button from the right in the buttons along the bottom. Once you've copied the curve you can delete the first layer.
This seems like great and the correct advice. I'll try this method!
Alternatively, don't mess with scale at all.
Simply turn your aeroplane layer to be a 3d layer and animate it on the z-axis!
As you're new to AE, I'd suggest you start here first: http://adobe.ly/AE_basics
Thanks for the link and the great advice, I will try this method.