I'm reading this article about Tommy Burns http://www.boxingoverbroadway.com/tommy-burns-smallest-heavyweight-champ-packed-a-punch/ and it says he was 5'7 yet was a HW champ with 13 title defenses and 46 wins (34 by knockout), 4 losses (2 by stoppage), and 8 draws. How the heck could a 5'7 guy fighting at HW not only have 34 KOs, but win the championship and defend the title 13x? What was the height and weight range for HWs in those days? (I understand he fought in the 1910s)
Burns wasn't viewed as anything special in his times. The heavyweights before him Sullivan, Corbett, Fitzsimmons, Jeffries, and the heavyweights after him, Johnson, and Dempsey were viewed as better. In fact, many of the contenders were viewed as better.! All of the champions I named were taller, and almost all of them heavier. The best champions back ( 1890-1914 ) then ranged from 5-10' to 6'1 with an average weight of about 190 pounds. The only big one of the lot was Jeffries, who was 6'1 1/2 220 pounds. Burns was an analogy who came along at the right time and fought very easy competition in general as champion until Jack Johnson.
Worth noting a lot of Burn's earlier fights were at middleweight. A middleweight, or even welterweight, fighting heavyweights really wasn't uncommon back then, there was Light Heavyweights to some extent, but not really, middlweight was the next division down. You can't say the average size, because we don't have anything like enough information. It's interesting, so to give the weights over time John L Sullivan (champion of America from 1882, lost the world title in 1892) was 5' 10 1/2" and around 190-200Ibs Charlie Mitchell (champion of England claiment, and top challenger fighting Sullivan in 1883 and 1888) 5' 9 and around 140-160Ibs Peter Jackson (champion of Australia in 1886, world coloured champion in 1888, should have been world champion, and arguably was in the early 1890's) 6'1 1/2" around 190-200Ibs James J Corbett (world champion 1892-1897) was 6' 1" and around 178-188Ibs Peter Maher (arguable champion 1895-1896) 5′ 11½″ around 170-180Ibs Bob Fitzsimmons (world middleweight champion from 1891, world heavyweight champion 1897-1899, top contender until ~1904) 5′ 11½″ around 168Ibs Tom Sharkey (questionable title claims in 1896 and 1897 and challenged Jeffries in 1899) 5′ 8″ around 170-180Ibs Gus Ruhlin (challenged Jeffries in 1901) 6' 2", 190-200Ibs James J Jeffries (world champion 1899-1904) 6′ 0″ around 200-230Ibs Marvin Hart (Questionable world champion 1905-1906) 5′ 11½″ around 190Ibs Tommy Burns (world champion 1906-1908) 5′ 7″ around 168-182 Jack Johnson (world colored champion 1902, world champion 1908-1915) 6′ 0½″ around 190-220Ibs Philidephia Jack O'Brien (Former Middleweight champion claimant, Light Heavyweight champion, and world champion claimant from 1905, challenged Tommy Burns in 1906 and 1907, and fought Jack Johnson in 1909), 5′ 10½″, 160-168Ibs Sam Langford (challenged for the colored championship 1906-1920, winning it multiple times from 1909-1918) 5′ 7½″ around 156-204Ibs Joe Jeanette (challenged for the colored championship 1906-1919, winning it multiple times from 1909-1916) 5′ 10″ around 185-200Ibs Sam McVea (challenged for the colored championship 1903-1920, winning it multiple times from 1909-1915) 5′ 10½″, around 197-220Ibs Fireman Jim Flynn (challenged for the world championship in 1912) 5′ 10½″ around 180-190Ibs Frank Moran (challenged for the world title in 1914 and 1916) 6′ 1½″ around 190-210Ibs Harry Wills (world colored champion 1915-1915 and from 1918, top challenger until 1926) 6′ 2″ around 200-225Ibs Jess Willard (world champion 1915-1919) 6′ 6½″ around 225-245Ibs Jack Dempsery (world champion 1919-1926) 6′ 1″ around 185-195Ibs I should note, it's not uncommon at all for multiple heights to be given for the same person, even now, and the weights were often just stated or estimated, rather than properly weighed in. There are plenty more I'd like to include, and probably several I've forgotten, but, enough for now. . .
From 1884 until 1889 the heavyweight champion of South Africa was 5′ 6″ and weighed 144-155Ibs. James Robertson Couper, interesting guy, but there's little information on him in English. http://supersport.dstv.com/boxing/features/news/160225/SAs_first_superfight