Make the game interesting. In Link to the Past, the best part was all the dungeons were open at any given time. I used to get through a dungeon mid way, get the big treasure chest (say an ice rod), leave, take it to the fire dungeon and whoop butt. You could separate the game by having certain parts only passable with certain weapons to keep it somewhat linear.

The weapons could still be limited selection but upgraded for new abilities. Stronger swords. Multiple Arrows. Throw bombs further. Jump higher. Lift heavier. Use different spells. It can be done.

And I really liked the magical medallions from Link the to Past. All of this is possible. We have games now with such open ended worlds and an, almost, endless array of weapons and spells. It can be done.

Zelda games used to be one of my favorite type of games but now lately it is all childish and features the same weapons over and over.

I see where people are worried that it would change the genre. But I do not think so. People are viewing this way too much like grinding or spending time to level up. I tried to make it as clear as possible that I did not support that idea and was wanting it done in subtle ways throughout the game that would go off of gamer habits.

Now, I'm not completely against a leveling system for a Zelda game but I'm trying to reiterate to you what NachoKingP said, that the things you are asking for are in some way already present in the current series. Here is something that would have been cool to level up in the Zelda series and since I was a huge fan of Ocarina I'll make reference to it. I think that Link's magical abilities would have been a great aspect to level up. Let's take Din's fire for example. It was fun to use but it would have been interesting to level it up in ways that lets you use it differently. Maybe allow it to light your sword on fire to add damage, shoot a fireball at an enemy (I did not forget about the fire arrows, I just think it would be cool to shoot one from your hands), and maybe a flame thrower ability.

Here is something that I really want in a current Zelda series. Pegasus Boots. I have much love for Epona but I really want to dash across the world at high speeds.

If you were to change the leveling mechanic of a Zelda title, it would change the genre of the game. The way Zelda has always played is that he must find a certain item that allows him to defeat whatever obstacle is preventing him from moving on through the story. As the levels advance, the puzzles require more complicated uses of the items, or a combination of items to solce puzzles. If Link was given multiple ways to advance past a point in the story, it would fundamentally change the dynamic of what I've always loved about the LoZ series. If you're given the option to get an item to advance the story, or to use Intelligence to get past the obstacle another way, then you lose the ability to build into later stages of the game the need for using that item, and the entire structure of the game then must be changed to accommodate that lost item.

There are very few games that follow the same structure as the LoZ has, and I'm happy about that. Changing it from what it is to fit the structure of what so many other Western RPGs already are would be a huge mistake and ultimately ruin the experience for the millions of fans that love this series and continually vote the games in the series some of the best games in history.