Why wasn't the timeline affected any further from the events in the season 1 finale?

It doesn't follow a single one. It's both Back to the Future and Terminator and 12 Monkeys, as Cisco explained to Joe, and others. Time travelers are somewhat immune to changes they make themselves. As in Back to the Future, changes to Marty's past won't change his personality as they logically should, nor does it change his memories, but they can threaten his physical existence.

The Executive Producer Andrew Kreisberg said in an interview:

How does Eddie's sacrifice work? Eobard disappears — but everything he did up until the finale still happened?

Our time travel hopefully holds together as much as it can. It doesn't completely obliterate all of their memories of Eddie [Eobard? -cde] and everything, but it has the desired effect of "harm to Eddie means harm to Tom Cavanagh's character [Eobard]."

An obvious non-answer, it doesn't explain anything the show hasn't already shown.

As concerned as the show and characters are about the consequences of time travel, as seen by Eobard desperate to change or keep the future intact, and the events of "Rogue Time" after Barry jumped just a day back in time, I'm certain it won't go unexplained.

Update:

Episodes in the following season seem to cement the Back to the Future usage more than anything. Specifically, s02e11 "The Reverse-Flash Returns":

Joe: Eddie Thawne died, so Eobard Thawne should have been erased out of existence, right?
Wells-2: Not necessarily. It's possible Eobard was in the Speed Force, protecting him like a bomb shelter, keeping him alive and his time line intact. It's what's known as a “Timeline Remnant”.
... Joe: If Thawne dies before he can time travel again, will that save Barry's mother?
Wells-2: No. That's not how it works. In our time line, Barry's mother is already dead, and her death is a fixed point. Nothing can change that.

He then draws a BTTF like diagram. These scientists and their constant diagrams. Note that circle 1 is Eobard's death, Circle 2 is the Present, Circle 3 is Eobard's birth.

The episode continues with a younger, pre-Barry's-Mom's-Death Eobard. When Barry attempts to change things, to prevent his Mother's Death, the show takes a Back to the Future route and starts to erase Cisco from the present (like Marty was in BTTF 2), until Barry ensures that Eobard is free to do what he already having been going to do.

In a later episode, s02e17 "Flash Back", Barry once again changes the past in ways that create bootstrap/information/grandfather paradoxes, more Terminator like.

So in short, time-travel works in The Flash the way it works in most mediums, as conveniently as the writers want it to be. There is no consistency, except that Speedsters tend to be protected from time changes, by the Speed Force. This is regularly used in the source comics as well. It may be an issue of some events being more important. A Doctor Who like "wibbly wobbly timey whimey" theory of time travel. Some are Fixed Points that have to happen or will always happen, some are in constant flux and can always change. Wells-2 use of the term "fixed point" alludes to this.

A side note. Single day jumps. Barry has jumped back a single day in time twice, once during "Rogue Time" and again during the Arrow/Legends of Tomorrow Crossover "Legends of Tomorrow". Both of these times, he A) jumps back a very short period of time, B) Jumps back after a massive death event, and C) Jumps back with the intent to change time. These short jumps, maybe due to the intent or the shortness of it, result in Time punishing the changes, and Flash merging or taking over the previous timeline version, which can only be assumed to be removing a Timeline Remnant from existence/creation. So these jumps are special compared to the longer ones involving years or decades.

Because these was a singularity that protected Reverse Flash in speed force and his deeds.

Sorry I now realized that your present action can lead to future changes but not your past.

When Eddie killed himself he changed the future not the events that happened in past.