What kind of weak signal? What is the voltage range of the signal? What is the output impedance of the signal source? Is the signal differential or single-ended? How many times do you want to amplify the signal?

The following figure shows a two-stage in-phase amplification circuit, and it is recommended that the first stage amplification be set to 50, and the second stage amplification be set to 20, so that the total amplification is 1000.

The single-stage amplification is determined by the proportionality resistor (R2+R1)/R1.

The TL062 is not considered to be a very high precision op-amp, its typical value of the offset voltage is 3mV, and the maximum value is up to 15mV, so it is recommended that the voltage gain of the first stage is appropriately large, so that the second stage of the op-amp's offset voltage will have less impact.

I suggest you use the TLC2262, an op-amp with an offset voltage of only 300μV typical, 2.5mV maximum, and a higher input impedance than the TL062, and a full-amplitude output op-amp, pin-for-pin compatible with the TL062. The only drawback is that the supply voltage range is 0~16V (TL062 is 10~30V), but if you don't require the signal to be amplified to more than 16V, it works perfectly.