From what I understand, すぎ means too much, till the point it is bad. For example 食べすぎ would mean "eating way too much (and it's not good)". So how would one say "eating too much (and it's good)"? Can すぎ be used here? Or a better example, "I love my wife too much (and it is a good thing)". Would 好きすぎ make it sound like it's a bad thing to love my wife too much?
I think the usage of すぎる parallels that of "too much" — usually "too much" means that it's "so much that it's something negative".
But colloquially, this can be used for emphasis, as in "so much that it is (almost) too much", meaning "very much" but in a positive (rather than a negative) way. (See also What does できなさすぎる mean?)
For example, if you say
it will (in the right context) be understood as something positive, just like "it was so good that I ate too much". Similarly,
I love him/her so much it's bad
No, adding すぎる to the end of a noun, verb, or adjective does not necessarily imply that being too much of something is bad, though we generally only use it this way colloquially.
He's so mature and I really respect him for that.
I love my wife's cooking soooo f**king much!!
That dog we just passed was sooooo cute!
It all depends on context.
As others have noted, すぎ can imply both depending on the contest. But it's mostly used in a positive way.
For example 食べすぎ would mean "eating way too much (and it's not good)"
If you want to express regret from the action that you did, you can use the て form + しまう.
This form is used to express an action that has taken place unintentionally with unsatisfactory results.
I eat too much. (you regret it because you think it's unhealthy or you are going to gain weight. No matter what the reason is)
Note しまう cannot be used to express regret concerning an action not taking place. For instance, you cannot use it to say "Regrettably, X didn't take place" or "Unfortunately, I didn't do X"
Edit "You use すぎる when something is beyond normal or proper, suggesting that you do not welcome it. Thus 親切すぎます (too kind) for example is not a straightforward compliment. Use modifiers like とても and すごく if you simply want to say that something is in a high degree."
Source Genki 1 Page 272