They call me Inspector Morse

Java (JDK), 131 124 110 84 64 bytes

Interestingly, "dot" is dash-heavy and "dash" is dot-heavy.

Takes input in all caps as an IntStream (scroll down for a version with an actual String for an extra 8 bytes). I've had quite a lot of help golfing this one: Thanks to Expired Data for golfing 20 bytes, to Neil for golfing 26 bytes, to Olivier Grégoire for golfing 18 bytes and to Kevin Cruijssen for golfing 2 bytes.

Contains 26 unprintable characters inside the double quotes.

c->c.map(a->"".charAt(a-65)-4).sum()>0

Try it online!

Ungolfed:

c -> // lambda taking input as an IntStream in upper case and returning a boolean
  c.map(a -> "" // map each character's ASCII value to its net dot impact (unprintable characters here)
    .charAt(a - 65) // translate the ASCII code into a zero-based index into the above string (65 is 'A')
    - 4) // unprintables are > 0, this restores the proper values
  .sum() > 0 // add up all the values, positive sum indicates a dot-heavy input string

Java (JDK), 131 124 110 84 72 bytes

For purists; takes input as a String. Thanks to Expired Data for golfing 20 bytes, to Neil for golfing 26 bytes and to Olivier Grégoire for golfing 10 bytes.

s->s.chars().map(a->"".charAt(a-65)-4).sum()>0

Try it online.

Ungolfed:

s -> // lambda taking input as a String in upper case and returning a boolean
  s.chars() // convert to a stream of characters
  .map(a -> "" // map each character's ASCII value to its net dot impact (unprintable characters here)
    .charAt(a - 65) // translate the ASCII code into a zero-based index into the above string (65 is 'A')
    - 4) // unprintables are > 0, this restores the proper values
  .sum() > 0 // add up all the values, positive sum indicates a dot-heavy input string

IBM PC DOS, 8088 assembly, 54 35 bytes

-19 bytes using the difference method

ac2c 41d0 d8d7 7206 51b1 04d2 e859 240f 2c03 02e0 e2ea 3534 4527 4125 1303 1462 4523 13

Unassembled:

; compare dashes and dots in a morse code string
; input:
;   I: pointer to input string (default SI)
;   IL: length of input string (default CX)
;   TBL: pointer to data table (default BX)
; output:
;   Sign/OF flags: Dot-heavy: SF == OF (JGE), Dash-heavy: SF != OF (JL)
MORSE_DD    MACRO   I, IL, TBL
            LOCAL   LOOP_LETTER, ODD
        IFDIFI <I>,<SI>     ; skip if S is already SI
    MOV  SI, I              ; load string into SI 
        ENDIF
        IFDIFI <IL>,<CX>    ; skip if IL is already CX
    MOV  CX, IL             ; set up loop counter
        ENDIF
        IFDIFI <TBL>,<BX>   ; skip if TBL is already BX
    MOV  BX, OFFSET TBL     ; load letter table into BX
        ENDIF
LOOP_LETTER:
    LODSB                   ; load next char from DS:SI into AL, advance SI
    ;AND  AL, 0DFH           ; uppercase the input letter (+2 bytes)
    SUB  AL, 'A'            ; convert letter to zero-based index
    RCR  AL, 1              ; divide index by 2, set CF if odd index
    XLAT                    ; lookup letter in table
    JC   ODD                ; if odd index use low nibble; if even use high nibble
    PUSH CX                 ; save loop counter (since SHR can only take CL on 8088)
    MOV  CL, 4              ; set up right shift for 4 bits
    SHR  AL, CL             ; shift right
    POP  CX                 ; restore loop counter
ODD:
    AND  AL, 0FH            ; mask low nibble
    SUB  AL, 3              ; unbias dash/dot difference +3 positive
    ADD  AH, AL             ; add letter difference to sum (set result flags)
    LOOP LOOP_LETTER
        ENDM

TBL DB 035H, 034H, 045H, 027H, 041H, 025H, 013H, 003H, 014H, 062H, 045H, 023H, 013H

Explanation

Implemented in Intel/MASM syntax as a MACRO (basically a function), using only 8088 compatible instructions. Input as uppercase string (or +2 bytes to allow mixed-case), output Truthy/Falsy result is SF == OF (use JG or JL to test).

The letter difference table values are stored as binary nibbles, so only takes 13 bytes in total.

Original (54 bytes):

; compare dashes and dots in a Morse code string
; input:
;   I: pointer to input string (default SI)
;   IL: length of input string (default CX)
;   TBL: pointer to data table
; output:
;   Carry Flag: CF=1 (CY) if dot-heavy, CF=0 (NC) if dash-heavy
MORSE_DD    MACRO   I, IL, TBL
            LOCAL   LOOP_LETTER
        IFDIFI <I>,<SI>     ; skip if S is already SI
    MOV  SI, I              ; load string into SI 
        ENDIF
        IFDIFI <IL>,<CX>    ; skip if IL is already CX
    MOV  CX, IL             ; set up loop counter
        ENDIF
    MOV  BX, OFFSET TBL     ; load score table into BX
    XOR  DX, DX             ; clear DX to hold total score
LOOP_LETTER:
    LODSB                   ; load next char from DS:SI into AL, advance SI
    ;AND  AL, 0DFH           ; uppercase the input letter (+2 bytes)
    SUB  AL, 'A'            ; convert letter to zero-based index
    XLAT                    ; lookup letter in table
    MOV  AH, AL             ; examine dot nibble
    AND  AH, 0FH            ; mask off dash nibble
    ADD  DH, AH             ; add letter dot count to total
    PUSH CX                 ; save loop counter (since SHR can only take CL)
    MOV  CL, 4              ; set up right shift for 4 bits
    SHR  AL, CL             ; shift right
    POP  CX                 ; restore loop counter
    ADD  DL, AL             ; add letter dash count to total
    LOOP LOOP_LETTER
    CMP  DL, DH             ; if dot-heavy CF=1, if dash-heavy CF=0
        ENDM

; data table A-Z: MSN = count of dash, LSN = count of dot
TBL DB 011H, 013H, 022H, 012H, 001H, 013H, 021H, 004H, 002H 
    DB 031H, 021H, 013H, 020H, 011H, 030H, 022H, 031H, 012H
    DB 003H, 010H, 012H, 013H, 021H, 022H, 031H, 022H

Explanation

Implemented in Intel/MASM syntax as a MACRO (basically a function), using only 8088 compatible instructions. Input as string, output Truthy/Falsy result in Carry Flag. Score table contains the number of dashes and dots per letter.

Input is upper case. Add 2 bytes to take lower or mixed case.

Example Test Program (as IBM PC DOS standalone COM executable)

    SHR  SI, 1              ; point SI to DOS PSP
    LODSW                   ; load arg length into AL, advance SI to 82H
    MOV  CL, AL             ; set up loop counter in CH
    DEC  CX                 ; remove leading space from letter count

    MORSE_DD SI, CX, TBL    ; execute above function, result is in CF

    MOV  DX, OFFSET F       ; default output to "Falsy" string
    JA   DISP_OUT           ; if CF=0, result is falsy, skip to output
    MOV  DX, OFFSET T       ; otherwise CF=1, set output to "Truthy" string
DISP_OUT:
    MOV  AH, 09H            ; DOS API display string function
    INT  21H
    RET

T   DB "Truthy$"
F   DB "Falsy$"

Example Output:

enter image description here

Download test program DD.COM

Or Try it Online! I'm not aware of an online TIO to direct link to a DOS executable, however you can use this with just a few steps:

  1. Download DD.COM as a ZIP file
  2. Go to https://virtualconsoles.com/online-emulators/DOS/
  3. Upload the ZIP file you just downloaded, click Start
  4. Type DD Hello or DD code to your heart's content

APL (Dyalog Extended), 24 15 bytesSBCS

-9 thanks to Ven

Anonymous tacit prefix function taking uppercase as argument.

>/'.-'⍧∊∘⌂morse

Try it online!

⌂morse convert to list of Morse strings
 then
ϵnlist (flatten)
'.-'⍧ count the number of dots and dashes in that
>/ more dots than dashes? (lit. greater-than reduction)