I see no connection there, just a statement that high-energy particles have an increased mass. And that is only true when observing the particle from another frame of reference; if you were moving with the particle, it would not appear to you to have an increased mass.
The strong force does not yet show any sign of being affected by increased mass or gravity. I have some experience with particle acceleration myself, namely with Fermilab data. Particle acceleration does not weaken the strong force, as I believe you are trying to infer from the said statement, but rather is a probe for studying it.
Gravity of any valid strength should have little or no bearing on the formation of tetraquarks. X(3872), as it is called, is confined by its wave-function, not by gravity.
Either elaborate more on your idea, or quote more of the said passage from Hawking word for word so that we can get an idea of the context. And remember, Hawking is a theorist, not an experimentalist.