Allan Trammell was 6'0 and weighed 165 pounds and managed to win four Gold Gloves and three Sliver Sluggers in his career at Shortstop.
He wasn't a "big man" at all and did just fine. The stereotypes of having to be a certain height or weight are stupid.
Notable Seasons
1990: .304 AVG, 14 HRs, 89 RBIs, .377 OBP, won a Sliver Slugger
1988: .311 AVG, 15 HRs, 69 RBIs, .373 OBP, won a Sliver Slugger
1987: .343 AVG, 28 HRs, 105 RBIs, second in MVP voting, won a Sliver Slugger
1986: .277 AVG, 21 HRs, 75 RBIs
1984: .314 AVG, 14 HRs, 69 RBIs, .382 OBP
1983: .319 AVG, 14 HRs, 66 RBIs, 30 SB, .385 OBP
Yeah, not too shabby for a non-"big man".