Tempi are only important if the moves are useful for development, which the pawn moves aren't.
Why is the Ruy Lopez good?

I never play this opening anymore...but appearently White is suppose to put pressure on the e5 pawn, making Black concide a space disadvantage by playing e6 or lose "time" defending that pawn, in some other manner. So gradually White will be able to gain an advantage in the center.
Or so says the Dude on ChessOpenings.Com. ;-)
Well the key reason is that bishops are stronger when they are further ayway from the battlefield.
- Ruy Lopez -- After a6 and b5 the bischop ends on b3 putting pressure on the weak spot of black f7 (btw black plays these moves to avoid annoying pressure on e5 as white can choose if and when to exchange on c6)
- Italian game -- The bishop directly goes to c4 and puts presure on the f7 pawn.
The idea between the openings is the same put presure on the weak spot but in the ruy lopez this is done from b3 (further away from the battlefield) while in italian this is done from c4. Closer to the battle field.
In the old lines of the Italian white would play c3 and d4 (like he still does in most of the lines in the ruy lopez) and build up a strong center position.
However .. when white finally manages to play d4 in the italian game black can calmly take on d4 and then play d5 "forking" the pawn on e4 and the bischop on c4 forcing white to take. If instead his bischop would be on b3 the counter strike d5 would not be a treath as it does not fork anything and white idoes not take on d5 instead he plays e5 with an advantage.

Tempi are only important if the moves are useful for development, which the pawn moves aren't.
I'm no titled player, but pretty much this. Pawn moves don't count as development. The moves a6 and b5 are both a weakness and a strength, meanwhile the a2-g8 diagonal is not a liability for white's bishop. And so, like many popular openings, begins a dynamic struggle. Black trying to make use of his expanding queenside and white to attack on the kingside. Also the center can be opened, white may undermine black's queenside, and black may even aim at the center and white's kingside himself in some variations.
Anyway the short answer is that the pawn moves are double edged having both good and bad points and in practice it's shown to lead to a dynamic struggle.

Every pawn move makes a hole that something must cover (either another piece or a pawn) as well as give the advancing player an advantage in space.
I have found that a weakness is only a weakness if you can exploit it. For example let's say in a line where Black plays Bg4 having a backup Knight on f6 and White plays h3 with the Bishop going to h5 and then White plays g4 next, Black can play Nxg4 and after hxg4 play Bxg4, the whole King side catled position is unmasked and Black still has the pin on the Queen.
Another is in the Philidor after 1. e4 e5 2. Nf3 d6 3. d4 Bg4 4. dxe5 there is a trap if Black plays 4... dxe5 5. Qxd8+ Kxd8 but if Black plays 4... Bxf3 then White has 5. Qxf3 dxe5 6. Bc4 Nf6 and 7. Qb3, attacking b7 and f7 since the d pawn went to d6 opening the lines up.
Most players of any good strength will make likely 2-3 pawn moves in the opening and try to get the pieces devloped. Wafflemaster is correct in assessing that pawn moves are specifically developing moves. An exception to this might be in Hypermodern systems or closed games like the Saemisch King's Indian.

Here's an example... a recent rated match game that I played. Black responded with an early ... a6 and ... b5, driving my Bishop back to the b3 square, but it turned out that this Pawn advance had only weakened his Q-side formation and driven my Bishop to a better square.

While not a Ruy Lopez, here is an example of how not to use the pawns.
B60: Sicilian Defense-Richter-Rauzer: Bonderevski Variation (if that is how you spell it. 15+10
Every pawn move makes a hole that something must cover (either another piece or a pawn) as well as give the advancing player an advantage in space.
I have found that a weakness is only a weakness if you can exploit it. For example let's say in a line where Black plays Bg4 having a backup Knight on f6 and White plays h3 with the Bishop going to h5 and then White plays g4 next, Black can play Nxg4 and after hxg4 play Bxg4, the whole King side catled position is unmasked and Black still has the pin on the Queen.
Another is in the Philidor after 1. e4 e5 2. Nf3 d6 3. d4 Bg4 4. dxe5 there is a trap if Black plays 4... dxe5 5. Qxd8+ Kxd8 but if Black plays 4... Bxf3 then White has 5. Qxf3 dxe5 6. Bc4 Nf6 and 7. Qb3, attacking b7 and f7 since the d pawn went to d6 opening the lines up.
Most players of any good strength will make likely 2-3 pawn moves in the opening and try to get the pieces devloped. Wafflemaster is correct in assessing that pawn moves are specifically developing moves. An exception to this might be in Hypermodern systems or closed games like the Saemisch King's Indian.
Are you sure that you found out that a weakness is only a weakness when you can exploit it?? Im pretty sure that its the invention of someone else

just kidding im bored
No you are correct, someone else likely discovered that. But at least it only took a couple thousand losses to get it to sink in.

Well the key reason is that bishops are stronger when they are further ayway from the battlefield.
Ruy Lopez -- After a6 and b5 the bischop ends on b3 putting pressure on the weak spot of black f7 (btw black plays these moves to avoid annoying pressure on e5 as white can choose if and when to exchange on c6) Italian game -- The bishop directly goes to c4 and puts presure on the f7 pawn.The idea between the openings is the same put presure on the weak spot but in the ruy lopez this is done from b3 (further away from the battlefield) while in italian this is done from c4. Closer to the battle field.
In the old lines of the Italian white would play c3 and d4 (like he still does in most of the lines in the ruy lopez) and build up a strong center position.
However .. when white finally manages to play d4 in the italian game black can calmly take on d4 and then play d5 "forking" the pawn on e4 and the bischop on c4 forcing white to take. If instead his bischop would be on b3 the counter strike d5 would not be a treath as it does not fork anything and white idoes not take on d5 instead he plays e5 with an advantage.
In the Ruy Lopez after 5. Bb3 Bc5
6.Bxf7 get a good attack going
@Coyotoloco:
The move order i gave against the Ruy Lopez certainly is not blacks best try for equality but i used it to prove a point that white would rather have his bischop placed on b3 (like in the ruy lopez) than on c4 (in the italian) so i used a similar position.
The move Bxf7 however is a silly sacrafice that leaves white with virtually no compensation for his piece. White certainly is not developed well enough to make use of the open black king position.

The ruy lopez is good b/c it is like a more agressive version of the italian game.
Not sure I agree. The Evans gambit or Fried Liver are aggressive versions of the Italian game.
The Ruy is more like a long positional struggle than an aggressive opening. Eventually you may play for an attack, but it's very slow getting there.
I have tried this opening and it just seems to cost you tempi when your bishop is threatened. Then black has advanced his pawns and white is no better off than they started.
Obviously, given statistics I am wrong, but I can't figure out why. I've looked at a lot of games and commentary and nothing really sticks out. Is it only sucessful as an advanced player?