Generally, an assertion is tagged for one of two reasons. First, the above phraseology is generally used as a defense mechanism. That is, if someone challenges me in my asserted proposition, then I can always find comfort in the notion that, "well, at least that's what I believe" and the challenger then generally backs off (to do otherwise would be social taboo, or so we are told).
Second--and really an answer to the question of why the first reason above is such a successful tactic in our culture--is that the phrase "at least to me" truly embodies the relativistic mindset. Such and such may be true absolutely; but, even if it is not, then it is certainly true to me--and you have no standing to challenge the claim that it is true to me. Who am I to challenge the truth value of the views that one personally holds? Or so the argument goes. This mindset rejects the authority and existence of absolute truth. What we are left with, then, are competing claims of "truth," none of which are objectively verifiable. The consequence of such a scenario is, ultimately, an unfortunate power struggle.
I have made a concerted effort to prune this line of phraseology from my vocabulary--both because I want to be able to defend my positions without resorting to such a tactic and, more importantly, because of the dangers of a relativistic mindset. I hope you will do the same.
Soli Deo Gloria.