Let’s think of a bullet and a gun. While the bullet itself is not heavy at all, when you use a gun and shoot it, the bullet now appears to have gained mass and is now able to create a hole in the wall.

The bullet itself didn’t gain mass, but its kinetic energy makes it seem to have gained mass. It takes a lot more energy to make it stop the faster it goes.
If the bullet is going at the speed of light, it doesn’t weight more, but it’s kinetic energy makes it seem to have gain infinite mass. It will take infinite energy to make it stop, or go faster.
Since it’s real mass didn’t change, it cannot generate more gravity than when it’s not moving. Also it cannot become a black hole.

Well I’m no scientist but this is how I understand the physic behind it. Let me know if I’m lost in the void of stupidity. And also I hope my English is good enough so you guys understand.

And @Joe i agree agree to your reply. In simple terms you could say;
When the Universe was aged 380,000 years, it was dense and its temp was 3,000K. Imagine a small portion in the Universe sized 42 million lightyears which became our observable Universe today. The redshift of the CMB is about 1,090. This means that the Universe’s density went down by a factor of 1,090. It also means its temp dropped by a factor of 1,090 (3,000K / 1,090 = 2.75K). And its (our observable part) size growed by a factor of 1,090 (42mln ly * 1,090 = 45,780,000,000 ly or 45 billion ly radius)

But not with the part about the expansion happening everywhere 🙂
I calculated it once. If the Milky Way was expanding with space, it would do so at a rate of 2.15km/s. That sounds like alot, but its diameter would grow by about half an Astronomical Unit in one year. We could not measure it when we wanted to. This suggest that indeed the expansion might take place locally too. But its not. If you calculate it for our Solar System, you will find numbers that do not match. The distance Sun/Earth or AU increases by 20cm/year but it would be alot more if expansion took place here too. The Moon recedes 2.75cm/year but with an expansion “included” you get another number. Same go’s for the distance to the other planets. I am sorry, i cannot find my old notepad with calc’s, else i would have mention the exact numbers. Anyhow, expansion does occur locally, but it just passes by. The forces that keep matter together and gravity are so much stronger, expansion of space can’t hold a grip onto it….expanding space has no affect on it.