System Information
Operating system: not relevant
Graphics card: not relevant

Blender Version
3.0.0

Short description of error
One is able to map the size of a particle based on it's lifetime using a texture, but sizes (as well as other attributes) are not affected if the particles are keyed with relations. To re-iterate, the steps below as described work with Newtonian physics, but not keyed.

Exact steps for others to reproduce the error
Create a mesh to act as an emitter
Select your emitter and go to Properties > Particles, click New.
In Properties > Particles > Render, click Object and choose the object that will be emitted as particles and its size.
Duplicate the object and under Particles > Physics > Physics Type, select Keyed
In Particles > Physics > Relations, create two relations and set the two objects you have in your scene as new particle targets
Go to your 3D view and press alt A to launch a preview of your emission animation, then stop it somewhere in its course.
In Properties > Particles > Textures, add New and give it a name.
In Properties > Textures > Type, choose Blend.
In Properties > Textures > Colors, click Ramp.
In Properties > Textures > Mapping > Coordinate > choose Strand/Particles.
In Properties > Textures > Influences, unclick Time and enable Size.
In Properties > Textures > Colors, adjust the Ramp controller to increase or decrease the size of your emitted object over time.

Keyed Physics

No Physics