Plico means "to fold, roll, wind". Re- means "back, again", so replico means "to fold back, roll back, rewind". A sense "to roll over" is not very different; this no doubt developed from "roll back".
As it often happens, that concept could be used figuratively: "to roll something over in the mind". As rolling or folding an object or substance, such as a scroll, a braid, a toga, involves spending some time touching it and being able to inspect it from multiple angles, the figurative sense flows into "reflect upon [an idea]". (Cf. re-flecto "to bend back, turn back".) Re- suggests going over it again, so the sense of repetition lies in that praefix. When you reflect upon an idea, you think about it again and again; it's not just one simple act of thinking. Perhaps re- had a double effect: perhaps the step from "reflect on" to "repeat (in the mind)" was owing to the subconscious' taking the sense of repetition from re- into account a second time. Or perhaps it makes sense as a reinterpretation without duplicity. At any rate, the sense of repeat developed post-classically, so after the other senses, according to Lewis & Short.
As to replying, that originates in late juridical Latin (Lewis & Short). A reply means saying something back to the original utterance, so I think it is logical for that sense to be expressed by re- as well. As to why folding (back) came to mean uttering (back), I imagine the figurative sense "to roll something over in the mind" was expanded to rolling something over in a conversation, inspecting it by talking about it.
The full entry on replico from Lewis & Short:
rĕ-plĭco, āvi (e. g. Vulg. Gen. 4, 27; id. Jos.
8, 35 al.), ātum (collat. form, replictae tunicae, Stat. S. 4,
9, 29), 1, v. a., to fold or roll back, to bend or turn back
(cf.: revolvo, reflecto).
I. Lit.: vel Euhemero replicato, vel Nicagorā, etc., unrolled, opened, Arn. 4, 147; cf. infra, II.: surculos in terram
dimittito replicatoque ad vitis caput, bend back, Cato, R. R. 41, 4;
so, labra, Quint. 11, 3, 81; cf.: replicatā cervice, Plin. 34,
8, 19, 80; and: margine intus replicato, id. 9, 33, 52, 102: ab omni
laevitate acies radios tuos replicat, casts back, reflects, Sen. Q. N.
1, 3, 7; cf.: quia radii solis replicantur, id. ib. 2, 10, 3: jocinera
replicata, folded inwards, Suet. Aug. 95.—
II. Trop., to unfold, unroll, turn over; to bend or turn back; to open: ut ne replices annalium memoriam, unfold, turn over,
Cic. Sull. 9, 27; so, memoriam temporum, id. Leg. 3, 14, 41: traductio
temporis nihil novi efficientis et primum quicque replicantis,
unrolling, unwinding, id. Div. 1, 56, 127: cujus acumen nimis tenue
retunditur et in se saepe replicatur, is bent back, Sen. Ben. 1, 4, 1:
vestigium suum, to withdraw, i. e. to go back, App. M. 4, p. 151,
B. In partic.
1. To turn over and over in the mind, to think or reflect upon; to go over, repeat (post-class.): haec identidem mecum, App.
M. 3, p. 129: titulos, singula, Prud. στεφ. 11, 3: necem, to tell
again, Amm. 30, 1, 3: vitam, Sid. Ep. 7, 9: lamentum, Vulg. 2 Par. 35,
25; id. Num. 27, 23: quorum (glirium) magnitudo saepius replicata
laudatur adsidue, Amm. 28, 4, 13: vultu adsimulato saepius replicando,
quod, etc., id. 14, 11, 11. —
2. In jurid. and late Lat., to make a reply or replication, Dig. 2, 14, 35 fin.; Greg. Mag. in Job, 16 init.