Is leveling up my character with alchemy worth the time and effort?

I decided I wanted to spend a few hours leveling up my character (actual character level, not any one skill level). Smithing Dwarven stuff usually helps get the level meter up quick, but I was fresh out of ingots. Since I have a huge load of ingredients in my barrel at Riverwood, I took a huge stash of as much as me and my follower could carry and headed off to the alchemy shack. After concocting many potions with various ingredients, I noticed that my character's level meter wasn't really going up that much, although my alchemy skill was jumping levels like mad.

I have no real interest in alchemy in and of itself since the only potions I use are the ones that I find. That said, is it possible for alchemy to yield better results when it comes to raising my character's base level?

The speed at which skill levels help you gain character levels is proportional to your current skill level - there's a certain amount of "character experience" you gain per skill experience level gained.

Therefore, getting your Alchemy from 20 to 21 will do less for your overall level than getting, say, your Archery skill from 60 to 61.

The UESP article on leveling has the formulae for this:

XP required to level up your character = (Current level + 3) * 25

Leveling a skill gives you an amount of XP equivalent to the new level of the skill.

All skills level increases gain you character level experience in the same way though, so there's not a "better" or "worse" skill for gaining ranks in in order to level your character. (This of course ignores the fact that certain skills are easier than others to gain a skill level in.)

Since you're dealing with Alchemy, the amount of skill experience you gain is tied to the value of the items you create. If you want the fastest skill experience gains, craft the most expensive potions you can, regardless of their effects. For this, I'd recommend acquiring Giant Toes and mix them with Blue Mountain Flowers and Blue Butterfly Wings.

You increase character levels by increasing skill levels.

Increasing one skill from 20 to 23 gives (21+22+23) = 66 xp toward character level. This is the same as increasing one skill from 65 to 66.

It's not that smithing skill levels you faster than alchemy. It's that your first pumped skill leveled you through lower character levels, which require less character xp.

60 levels of smithing and 0 levels of alchemy yields the same character xp as 0 levels of smithing and 60 levels of alchemy.

Regardless of the order in which you learn skills, 60 levels of smithing + 60 levels of alchemy are worth the same character xp.

Given that each skill yields the same character xp as it levels, and that alchemy is fairly easy to level, it is definately "worth it" to level your character with alchemy.