Why do many languages tend to use plural forms to impart formality or deference?

As always, 'why' questions are a really bad idea in linguistics. You can reasonably ask these three types of questions:

1. Historical developments within a language
2. Areal / contact impact between languages
3. Hypothesized semantic motivations

Googling these three will actually give you plenty of results.

A quick search will reveal the following:

A: Historical and areal developments

1. The plural politeness (or T-V distinction as it is sometimes called) first developed in European languages in Latin.

2. It has spread through language contact to other European languages. For instance, English was influenced by French post Norman conquest.

3. Developments within individual languages have transformed the T-V expression of politeness/formality/social distance in various ways. For instance, making the plural 'you' in English the only form of address, using 3rd person plural in German (and from German extending it to Czech in the 19th century only for Czech to go back to T-V). Or the development of pan/pani (Mr/Mrs) + 3rd person sg in Polish.

B: Semantic motivations

There are several possible hypotheses as to the semantic motivation of the T-V distinction. These may differ across times and places, i.e. the original semantic motivation may not be the one that plays out in later times and places.

1. The origin of using a plural form of address is hypothesized to be in the address of the Roman Emperor in the time when the Roman Empire has two emperors (East and West). This is also where the Royal We may come from.

2. Speakers might also make sense of the form as indicating greater value in the plural (more means better) through a relationship of iconicity. (This could be a ex post explanation of some speakers).

3. The plural form could also be seen as creating a form of distance or indirectness similar to the use of past forms and other distancing circumlocutions in polite requests (I wonder if you could be so kind as to help me). In this sense, using the third person (whether plural as in German or singular as in Polish) would make the same semantic sense.

But note that plural forms can also be used to indicate intimacy between people who do not want to use informal forms as in the use of the first person plural. "Are we ready to have our meal." This can often be seen as a form of condescension.

Ultimately, semantic motivations are just that - motivations. They can develop in unpredictable ways across times, places and languages and therefore cannot be used for the sort of predictions a 'why' question may imply.