Does sperm weight causes sex ratio?

Chromosome X in female sperm is heavier than male Y chromosome. Does it causes difference in fertility of sperm and heavier female sperm is unable to fertilize better than male sperm?

This is given in AK Jain of physiology, chapter on reproduction. I doubt this explanation.

If motility is not the issue, you could imagine that, during the fertilization or insemination process, sperm might be under the force of gravity, leading to different sedimentation rates. A sperm's sedimentation speed is equal to the force on it divided by its friction coefficient $\gamma$, $$v_{sperm} = \frac{(m_{sperm}-m_{displaced}) g}{\gamma}$$ where $g$ is the gravitational acceleration and $m_{displaced}$ is the amount of mass displaced by the sperm. You can estimate $\gamma$ with Stokes' law (https://en.wikipedia.org/wiki/Stokes%27_law) as about $6\pi R \mu$ with $R$ being the sperm size and $\mu$ the fluid viscosity. We're interested in the maximum possible difference in speed, so we'll choose $R$ to be at the small scale of sperm size, $5$ microns and $\mu$ to be that of water $\mu \approx 0.01 \frac{g}{cm s}$. This gives us $\gamma \sim 10^{-4} g/s$. The difference between $v_X$ and $v_Y$ is then $$v_X - v_Y = \frac{(m_X - m_Y) g}{\gamma} \approx 0.01 \,\textrm{micron}/s$$