Many times in Halachic literature I have come across the formula in which one can follow the law more stringently than is necessary, and for that he will be blessed (תבא עליו ברכה). Does this formulation have a deeper Halachic and ancient tradition with more behind it, or is it simply a naive practice?
Prof. Benjamin Brown from University of Jerusalem published a paper about soft stringency in Halacha (more specific, on the Mishnah Berurah) in which he writes that this approach (can) have three different motivations, the jurisprudential, the social and the ideological. The paper is called "Soft Stringency in the Mishnah Brurah: The Jurisprudential, Sociological and Ideological Aspects of a Halakhic Formulation" and is available here, highly recommend having a look into it about this subject. I don't feel that me trying to summarize it here would do honor to the work, nor I have the time to do it.
Although if this is, in fact, the methodology adopted by the Mishnah Berura is debatable - see paper "The codification of Jewish Law and an introduction to the jurisprudence of the Mishna Berura" from professor Michael J. Broyde available here or the full book about it here - Brown's work continues to be an interesting resource about soft stringency in halacha.
The motivation for acting stringently is based primarily in יראת ה, or Fear of G-d. That is, one is careful not to do something that might transgress the will of G-d, even if it is ok according to the majority of authorities. As such, one would qualify for the blessings promised to those who fear G-d, for example:
יְר֣אוּ אֶת־יְהוָ֣ה קְדֹשָׁ֑יו כִּי־אֵ֥ין מַ֝חְס֗וֹר לִירֵאָֽיו׃
O fear the Lord, you saints of his: for those who fear him have no lack.