Google N-gram Corpus Counts
╭─ーーーー─┬────────┬───────╮
│ 重畳　　 │ 42,824 │ 79.1% │
│ 重畳して │  4,466 │  8.3% │
│ 重畳する │  3,792 │  7.0% │
│ 重畳です │    779 │  1.4% │
│ 重畳と　 │    694 │  1.3% │
│ 重畳の　 │    684 │  1.3% │
│ 重畳たる │    548 │  1.0% │
│ 重畳だ　 │    175 │  0.3% │
│ 重畳な　 │    167 │  0.3% │
╰─ーーーー─┴────────┴───────╯

ーーー Sense 1 ーーー
Sanseido's 現代外来語辞典 also supports [form]

In BCCWJ most examples (of 47 total) are sense one. In about one fifth of those hits, 重畳 is used as ～的, or part of another word.
[adv-to] appears thrice, [adj-t] once, [vs] 17 times (if I counted right).

In CSJ (also 47 examples) the hits are pretty much split between [vs] and "重畳-音声".
I guess 重畳-音声 could very well also be sense two, but in any case there are no [adj-t,adv-to] usages here.

Changes: [adj-t,adv-to,n,vs] ⇒ [n,vs,vi,adj-t,adv-to]; noun glosses
(While meikyo has [vt,vi] for sense one, no other kokugo does. On top of that the hits for "を重畳" in the NDL are overwhelmingly in technical works, suggesting that [vt] is better off on only sense two).

ーーー Sense 2 ーーー

ビジネス技術実用英語大辞典第4版 supports "superimposition"

Changes: [vi,vt] ⇒ [vt,vi]

ーーー Sense 3 ーーー
GendaiShinkoku supports [dated]

Massif examples are littered with sense three, the usage being mostly 形容動詞 (many with dropped copula)/感動詞.
https://massif.la/ja/search?q=重畳

While Iwakoku has its typical〘名ナノ〙tag, [adj-no] doesn't appear to be very common.
https://massif.la/ja/search?q=重畳の

Changes: [adj-no,adj-na,n,int] ⇒ [adj-na,int,n,adj-no]

.

Mostly reordering PoS tags.

@@ -14,0 +15,3 @@
+<pos>&n;</pos>
+<pos>&vs;</pos>
+<pos>&vi;</pos>
@@ -17,2 +19,0 @@
-<pos>&n;</pos>
-<pos>&vs;</pos>
@@ -20,2 +21,3 @@
-<gloss>placed one upon another</gloss>
-<gloss>piled up</gloss>
+<gloss>being placed one upon another</gloss>
+<gloss>piling up</gloss>
+<gloss>being atop another</gloss>
@@ -25,0 +28 @@
+<pos>&vt;</pos>
@@ -27 +29,0 @@
-<pos>&vt;</pos>
@@ -35,0 +38,3 @@
+<pos>&adj-na;</pos>
+<pos>&int;</pos>
+<pos>&n;</pos>
@@ -37,3 +41,0 @@
-<pos>&adj-na;</pos>
-<pos>&n;</pos>
-<pos>&int;</pos>
@@ -43,0 +46,2 @@
+<gloss>exquisite</gloss>
+<gloss>wonderful</gloss>

i probably should've explained the changes better, mb
add [rk] to じゅうじょう - only in gg5 (for sense 3) and nikk (for sense 1) and seems quite rare/outdated (nadeshiko, youglish)
sense 1:
add [form] - (sankoku, shinkoku)
add [n][vs][adv-to] - (sankoku, daijr/s, meikyo, shinkoku, etc.)
sense 2:
added relevant misc fields (as superimposition/superposition is somewhat technical)
added [vi][vt]
sense 3:
add [dated] - (sankoku, iwakoku)
add [adj-na] - (sankoku, iwakoku, obunsha, etc.)

sankoku, daijr/s, smk, meikyo, shinkoku, etc.

kokugos don't split sense 1 ("piling up") and 3 ("superimposition"), they're considered the same - having a reading restricted to just one of them seems weird
じゅうじょう is also only in gg5 (for sense 3) and nikk (for sense 1) and seems quite rare/outdated - i don't think it's needed

@@ -11,0 +12 @@
+<re_inf>&rk;</re_inf>
@@ -14 +14,0 @@
-<stagr>ちょうじょう</stagr>
@@ -15,0 +16,4 @@
+<pos>&adv-to;</pos>
+<pos>&n;</pos>
+<pos>&vs;</pos>
+<misc>&form;</misc>
@@ -19,0 +24,11 @@
+<pos>&n;</pos>
+<pos>&vs;</pos>
+<pos>&vi;</pos>
+<pos>&vt;</pos>
+<field>&physics;</field>
+<field>&elec;</field>
+<field>&comp;</field>
+<gloss>superimposition</gloss>
+<gloss>superposition</gloss>
+</sense>
+<sense>
@@ -21,0 +37 @@
+<pos>&adj-na;</pos>
@@ -23,0 +40 @@
+<misc>&dated;</misc>
@@ -26,6 +43 @@
-</sense>
-<sense>
-<pos>&n;</pos>
-<pos>&vs;</pos>
-<gloss>superimposition</gloss>
-<gloss>superposition</gloss>
+<gloss>satisfactory</gloss>