Joüon-Muraoka mention the doubled resh with regard to the interrogative heh in §102m:Moses Gummadi wrote: ↑Mon Sep 13, 2021 1:51 pm Hello, my name is Moses. I have no academic background in Theology, Hebrew or for that matter Humanities, but I am very interested in Biblical Hebrew. I taught myself Hebrew alphabet and vowels 9 years ago and spent significant time in developing computer code and analysing the text of the Tanach for things most scholars here would have no interest (eg. acrostics and other phenomenon) besides reading the Tanach.
I have been (self) studying Biblical Hebrew grammar for sometime now, and I like to test grammar rules on my computer (eg., I found these words with dagesh in Resh - הַרְּעִמָהּ הַרְּאִיתֶם רַּב רֹּאשׁ רֵּים רָּע לְשָׁרֶּךָ מָרַּת רַּךְ שֶׁרֹּאשִׁי כָרַּת שָׁרֵּךְ ) .
Paul Joüon and T. Muraoka, A Grammar of Biblical Hebrew (Roma: Pontificio Istituto Biblico, 2006), 308.Before shva (simple or nuanced), as the ḥaṭef pataḥ cannot be retained, we have ַ, e.g. הַבְרָכָה Lat. num benedictio? (= [is there] a blessing?) Gn 27.38; הַמְכַסֶּה Lat. num celans? (= [shall I] hide?) Gn 18.17 (comp. the same form with the article Lv 3.3 LXX: τὸ κατακαλύπτον that which conceals, § 35c). With the article there is virtual gemination; with the interrogative ה, which does not require gemination, there can, however, be virtual gemination, judging from the cases where there is genuine gemination. In some cases the consonant (even ר) is geminated, e.g. הַלְּבֶן Lat. num filio? (= to a son?) Gn 17.17; הַבְּדֶ֫רֶךְ Lat. num in via? (= in the way?) Ez 20.30; הַכְּתֹ֫נֶת Lat. num tunica? (= the tunic?) Gn 37.32; always הַרְּאִיתֶם Lat. num vidistis? (= surely you saw?) 1Sm 10.24; 17.25; 2Kg 6.32† (cf. § 23a).
Notice that it says that the situation of הֲ + רְאִיתֶם always results in הַרְּאִיתֶם, and then it lists the three verses in which it is found.
My supposition is that it is to mark the sheva as vocal, not to double the resh. That is, by placing the dagesh in the resh, you do not read it as har-ʾî-ṯém, but it makes the resh open the next syllable as ha-rə-ʾî-ṯém.