The British National Meteorological Office Library and Archives (NMLA) holds many ship weather reports. Included are a few Atlantic crossings to Quebec between 1869 and 1871, the early steamship era. They give an idea of how challenging the voyage might have been for landlubbers.
There are weather observations from vessels of the Allen Line, nine vessels across 36 separate voyages. The ships, with arrival dates at Quebec, are:
AUSTRIAN – Four voyages documented: June 6, July 18, August, and October 9, 1870
EUROPEAN – Three crossings available: July 25 and September 10, 1870; April 27 and June 20, 1871
HIBERNIAN – Four 1869 arrivals: May 24, July 5, August 16, and September 29
MORAVIAN – Seven voyages spanning two years: Five arrivals in 1869 (May 17, June 28, August 8, September 19) and three in 1870 (August 21, October 3 [two separate entries], November 13)
NESTORIAN – Five 1869 crossings: April 26, June 7, July 19, August 28, and October 10
OTTAWA – Four 1870 voyages: June 9, July 19, August, and October 12
PERUVIAN – Eight documented arrivals: Five in 1869 (May 31, July 10, August 23, October 4, November 16) and three in 1870 (August, September 26, November 9)
Find more details by searching ships meteorological log Quebec at https://library.metoffice.gov.uk/Portal/Default/en-GB/Search/SimpleSearch. The NMLA will send an image of the original records by email on request.
Manage your expectations — as shown by the extract below, the handwritten material can be faint and challenging to interpret. You should be able to discern from the winds, reported in the third column from the right on the Beaufort Scale, whether a voyage encountered rough weather.

Aside from the Peruvian, these ships were all of less than 2,500 tons, so passengers would have a hard time in heavy weather; that was my experience in a ship ten times the size.
I’d been hoping to be able to profile data from Global marine surface meteorological variables from 1851 to 2010 from comprehensive in-situ observations. However, for the past few days, there’s been a warning notice “Download form temporarily closed due to temporary issues reaching the data provider’s servers.” Could that data provider be affected by US government actions?