The beta 737 FMC seems to suggest a (landing optimised) take off weight of 43,600 kg.
It is really light for a take off, using the 737 Technical Site's data for an undefined 737 I got a V1 of about 120 knots and a V2 of about 131 knots with a take off distance of somewhere about 3,700 feet for sea level at 15 degrees C and with a 10 knot headwind using the 737 site's comprehensive Takeoff Field Limit Graph.
Petaluma in California's Runway 29 has a handy 3.600 feet runway and the light 737 sailed off early on full thrust, even on this exceptionally short runway.
Would it be possible to offer a much heavier option for simulating take offs?