What makes an opponents pieces/game weak?
Well, to begin with your ability to recognize and use the weaknesses in the position. Now generally speaking there are a few ways to measure an advantage based on the position:
1) Having the initiative (this loosely defined term generally corresponds to the ability to make threats and influence the (short-term) flow of the game).
2) Having superior coordination of the pieces - are your opponents pieces supporting each other, or is each of them performing an individual task? Can you disrupt their cordination? Oftentimes superior coordination and active play will compensate (at least for some time) a material disadvantage.
3) Pawn structure. Now this becomes rather important in the endgame but even in the middlegame one can take advantage of attacking an isolated pawne, etc.
4) The lack of clear plan. If you have a clear plan of improving your position and the opponent cannot prevent its execution, and lacks an alternative plan for getting counterplay (e.g if you attack kingside, he should struggle to attack queenside provided he cannot hope to deflect that atack) you have a technically won game.
5) Control of important strategical squares on the board. Pretty self-explanatory.
6) Material advantage - a big NOT ALWAYS. But generally speaking if you have an advantage in material, and the opponent cannot compensate it via 1), 2), or 5) you can easily win - just follow Capablanca's advice try to exchange all the pieces of equal value and simplify. 95% of the time this is the key to success, the other 5%, well, you'll learn to recognize them sooner or later.
7) A better tactical feel: Say you can calculate variations long 5 moves, and your opponent has a depth of 3. It is clear who'll have an edge. Tactics is a weapon that is flashy and must be used with caution - if it is not found on strategical advantage or a blunder on the opponents part it is usually unwise to get engaged in such trickery.
I hope that helps.