Are bulkier molecules more likely to react?
The relative rates are going to depend not on molecular weight so much but the structure of the molecule.

The specific reaction is also very important. 

Nucleophilic substitution reactions (some of the first reactions most students learn about in an organic chemistry course).

Let us compare 1-chlorobutane and 2-chloro-2-methylpropane, both $\ce{C4H9Cl}$. However, the 1-chlorobutane is a primary alkyl halide (not very bulky) and 2-chloro-2-methylpropane is a tertiary alkyl halide (bulky). 

The bulkier compound reacts faster in a solvolysis reaction:

$$\ce{(CH3)3CCl -&gt;[\ce{H2O}] (CH3)3COH}\ \ \mathrm{fast}$$
$$\ce{CH3CH2CH2CH2Cl -&gt;[\ce{H2O}] CH3CH2CH2CH2OH}\ \ \mathrm{slow\approx no\ reaction}$$

The reason that the tertiary halide reacts faster in this reaction is that its mechanism involves the formation of a carbocation intermediate and the extra carbon groups at the tertiary center provide more inductive stabilization to that carbocaion than the single alkyl group attached to a primary position. In general, in reactions that generate carbocation intermediates, tertiary substrates will react faster.

However, in many reactions bulkier molecules have steric interactions that negatively effect the rate. In a nucleophilic displacement with $\ce{NaI}$ in acetone, 1-chlorobutane will react faster.

$$\ce{(CH3)2CCl -&gt;[\ce{NaI}][\mathrm{acetone}](CH3)3CI}\ \ \mathrm{slow\approx no\ reaction}$$
$$\ce{CH3CH2CH2CH2Cl -&gt;[\ce{NaI}][\mathrm{acetone}]CH3CH2CH2CH2I}\ \ \mathrm{fast}$$