Okay can you please explain this further? So is everything in freefall, including the sun? Or are we freefalling towards the sun and the sun is stationary? Because if we are freefalling towards the sun then when we slingshot around it and head in the opposite direction that would be the opposite of freefalling, we would be travelling upwards, and against the sun's gravity at that. Actually that would be true even if we were travelling towards the sun horizontally when we slingshot around it and travel in the opposite direction we would be resisting the sun's gravity.
It gets more and more complicated as you consider more and more of reality.
The sun (the entire solar system actually) is in free fall around the galactic centre.
There are also various perterbations from other objects.
When just considering our solar system, the sun is effectively stationary (it actually wobbles a bit for each planet, which can be considered as the combination of the various orbits around the planet-sun barycenters, but that barycentre is well inside the sun).
And the sun determines what direction "down" is.
This means the sun is effectively in free fall around the sun.
But it isn't just falling down towards the sun, it is also moving sideways.
These movements combine to produce a roughly circular orbit.
Similar to how a ball on a string is constantly being pulled towards the centre by the string, but the sideways movement keeps it going in a circle instead of falling directly to it.
As I have said before (but not necessarily here):
Imagine an object following a circular path, which for simplicity of analysis is broken into 360 pieces.
It starts off half way along one of these peices travelling at a velocity of [0,100,0], at say a position of [100,0,0], and the direction of down is towards the centre, so in the direction [-1, 0, 0].
At the end of that piece, it needs to change direction to travel at a speed of 100 at a slight angle (1 degree off course).
This means it would now be travelling at [-1.74524064372835, 99.9847695156391, 0].
This represents a change in velocity of [-1.74524064372835, -0.0152304843608704, 0].
This is a change of 1.7453071, in the direction towards the centre of the circle.
So it has been accelerated towards the centre, or "down", to maintain a circular path.
This is simply how uniform circular motion works. In general, the acceleration required to maintain a circular path is given by v^2/r.
When Earth is on the other side of its orbit (corresponding to the hypothetical example having a velocity of [0, -100, 0], at a position [-100,0,0]) down is still towards the sun. This is a different direction to when Earth was on the other side. (the hypothetical example now has down being [1,0,0]).
As Earth travels around its orbit, down continues to point in the direction of the sun.